MATH225 Week 7 Assignment (30 Q/A) / MATH 225N Week 7 Assignment / MATH225 Week 7 Assignment / MATH225N Week 7 Assignment: Hypothesis Test for the mean-Polution Standard Deviation known (Latest, 2022): Chamberlain College of Nursing

MATH225 Week 7 Assignment (30 Q/A) / MATH 225N Week 7 Assignment / MATH225 Week 7 Assignment / MATH225N Week 7 Assignment: Hypothesis Test for the mean-Polution Standard Deviation known (Latest, 2022): Chamberlain College of Nursing MATH225N Week 7 Assignment: Hypothesis Test for the mean-Polution Standard Deviation known MATH225 Week 7 Assignment: Hypothesis Test for the mean-Polution Standard Deviation known Compute the value of the test statistic (z-value) for a hypothesis test for one population mean with a known standard deviation Question Jamie, a bowler, claims that her bowling score is less than 168 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She bowls 17 games. The mean score of the sample games is 155 points. Jamie knows from experience that the standard deviation for her bowling score is 19 points. • H0: μ≥168; Ha: μ168 • α=0.01 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? ________________________________________ Provide your answer: Test statistic =-2.82 Correct answers: • Test statistic = −2.82 The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean score, x¯=155. The sample the bowler uses is 17 games, so n=17. She knows the standard deviation of the games, σ=19. Lastly, the bowler is comparing the population mean score to 168points. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=155−√≈−134.608≈−2.82 So, the test statistic for this hypothesis test is z0=−2.82. Distinguish between one- and two-tailed hypotheses tests and understand possible conclusions Question Which graph below corresponds to the following hypothesis test? H0:μ≥5.9, Ha:μ5.9 Answer Explanation Correct answer: A normal curve is over a horizontal axis and is centered on 5.9. A vertical line segment extends from the horizontal axis to the curve at a point to the left of 5.9. The area under the curve to the left of the point is shaded. The alternative hypothesis, Ha, tells us which area of the graph we are interested in. Because the alternative hypothesis is μ5.9, we are interested in the region less than (to the left of) 5.9, so the correct graph is the first answer choice. Your answer: wrong Identify the null and alternative hypotheses Question A politician claims that at least 68% of voters support a decrease in taxes. A group of researchers are trying to show that this is not the case. Identify the researchers' null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p. ________________________________________ Select the correct answer below: ________________________________________ H0: p≤0.68; Ha: p0.68 H0: p0.68; Ha: p≥0.68 H0: p0.68; Ha: p≤0.68 H0: p≥0.68; Ha: p0.68 Perform and interpret a hypothesis test for a proportion using Technology - Excel Question Steve listens to his favorite streaming music service when he works out. He wonders whether the service's algorithm does a good job of finding random songs that he will like more often than not. To test this, he listens to 50 songs chosen by the service at random and finds that he likes 32 of them. Use Excel to test whether Steve will like a randomly selected song more often than not, and then draw a conclusion in the context of the problem. Use α=0.05. ________________________________________ Select the correct answer below: ________________________________________ Reject the null hypothesis. There is sufficient evidence to conclude that Steve will like a randomly selected song more often than not. Reject the null hypothesis. There is insufficient evidence to conclude that Steve will like a randomly selected song more often than not. Fail to reject the null hypothesis. There is sufficient evidence to conclude that Steve will like a randomly selected song more often than not. Fail to reject the null hypothesis. There is insufficient evidence to conclude that Steve will like a randomly selected song more often than not. Great work! That's correct.Correct answer: Reject the null hypothesis. There is sufficient evidence to conclude that Steve will like a randomly selected song more often than not. Step 1: The sample proportion is pˆ=3250=0.64, the hypothesized proportion is p0=0.5, and the sample size is n=50. Step 2: The test statistic, rounding to two decimal places, is z=0.64−0.50.5(1−0.5)50‾‾‾‾‾‾‾‾‾‾‾‾√≈1.98. Step 3: Since the test is right-tailed, entering the function =1−Norm.S.Dist(1.98,1) into Excel returns a p-value, rounding to three decimal places, of 0.024. Step 4: Since the p-value is less than α=0.05, reject the null hypothesis. There is sufficient evidence to conclude that Steve will like a randomly selected song more often than not. Null and alternative hypothesis: H0: p = 0.5 Ha: p = 0.5 Level of Significance =0.05 Proportion under H0 = 0.5 n = 50 Number of Successes=32 Sample Proportion 0.64000 StDev 0.50000 SE 0. Test Statistic (z) 1. One-Sided p-value 0. Two-Sided p-value 0. P value = 0.02 alpha (0.05) Hence, reject the null hypothesis. Perform and interpret a hypothesis test for a proportion using Technology - Excel Question A magazine regularly tested products and gave the reviews to its customers. In one of its reviews, it tested two types of batteries and claimed that the batteries from Company A outperformed the batteries from Company B. A representative from Company B asked for the exact data from the study. The author of the article told the representative from Company B that in 200 tests, a battery from Company A outperformed a battery from Company B in 108 of the tests. Company B decided to sue the magazine, claiming that the results were not significantly different from 50% and that the magazine was slandering its good name. Use Excel to test whether the true proportion of times that Company A's batteries outperformed Company B's batteries is different from 0.5. Identify the p-value, rounding to three decimal places. ________________________________________ Provide your answer below: ________________________________________ 0.258 p-value= Well done! You got it right.Correct answers: • p-value=0.258 Step 1: The sample proportion is pˆ==0.54, the hypothesized proportion is p0=0.5, and the sample size is n=200. Step 2: The test statistic, rounding to two decimal places, is z=0.54−0.50.5(1−0.5)200‾‾‾‾‾‾‾‾‾‾‾‾√≈1.13. Step 3: Since the test is two-tailed and the test statistic is positive, entering the function =2∗(1−Norm.S.Dist(1.13,1)) into Excel returns a p-value, rounding to three decimal places, of 0.258. Perform and interpret a hypothesis test for a proportion using Technology - Excel Question A candidate in an election lost by 5.8% of the vote. The candidate sued the state and said that more than 5.8% of the ballots were defective and not counted by the voting machine, so a full recount would need to be done. His opponent wanted to ask for the case to be dismissed, so she had a government official from the state randomly select 500 ballots and count how many were defective. The official found 45 defective ballots. Use Excel to test if the candidate's claim is true and that more than 5.8% of the ballots were defective. Identify the p-value, rounding to three decimal places. Well done! You got it right.Correct answers: • p-value=0.001 Step 1: The sample proportion is pˆ=45500=0.09, the hypothesized proportion is p0=0.058, and the sample size is n=500. Step 2: The test statistic, rounding to two decimal places, is z=0.09−0.0580.058(1−0.058)500‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√≈3.06. Step 3: Since the test is right-tailed, enter the function =Norm.S.Dist(3.06,0) into Excel and subtract from 1. This returns a p-value, rounding to three decimal places, of 0.001 Perform and interpret a hypothesis test for a proportion using Technology - Excel Question Dmitry suspected that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times. Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of odds is different from 50%. (a) Which answer choice shows the correct null and alternative hypotheses for this test? ________________________________________ Select the correct answer below: ________________________________________ H0:p=0.35; Ha:p0.35, which is a right-tailed test. H0:p=0.5; Ha:p0.5, which is a left-tailed test. H0:p=0.35; Ha:p≠0.35, which is a two-tailed test. H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. Well done! You got it right. Correct answer: H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. The null hypothesis should be true proportion: H0:p=0.5. Dmitry wants to know if the true proportion is different from 0.5. This means that we just want to test if the proportion is not 0.5. So, the alternative hypothesis is Ha:p≠0.5, which is a two-tailed test. PART 2 Perform and interpret a hypothesis test for a proportion using Technology - Excel Question Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times. Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of odds is different from 50%. (a) H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. (b) Use Excel to test whether the true proportion of odds is different from 50%. Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places. test statistic=-1.897 p-value=0.058 PART 3 Perform and interpret a hypothesis test for a proportion using Technology - Excel Question Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times. Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of odds is different from 50%. (a) H0:p=0.5; Ha:p≠0.5, which is a two-tailed test. (b) z0=−1.897, p-value is = 0.058 (c) Which of the following are appropriate conclusions for this hypothesis test? Select all that apply. ________________________________________ Select all that apply: ________________________________________ • We reject H0. • We fail to reject H0. • At the 5% significance level, the data provide sufficient evidence to conclude the true proportion of odds is different than 50%. • At the 5% significance level, the data do not provide sufficient evidence to conclude the true proportion of odds is different than 50%. • option 2 and 4 are answer • Explanation: • (c) From part b, p-value is = 0.058 0.05 significance level • So, we failed to reject the null hypothesis Ho • • And • At the 5% significance level, the data do not provide sufficient evidence to conclude the true proportion of odds is different than 50%. Identify the null and alternative hypotheses Question A politician claims that at least 68% of voters support a decrease in taxes. A group of researchers are trying to show that this is not the case. Identify the researchers' null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p. ________________________________________ Select the correct answer below: ________________________________________ H0: p≤0.68; Ha: p0.68 H0: p0.68; Ha: p≥0.68 H0: p0.68; Ha: p≤0.68 H0: p≥0.68; Ha: p0.68 4-H0: p≥0.68; Ha: p0.68 Explanation: First, the equal condition is written in the null hypothesis. Second, the statement that at least 68% of taxes support a decrease in taxes is expressed as: H0:P≥0.68 second, the alternative hypothesis is the investigation hypothesis, the opposite of the null hypothesis: Ha:P0.68 Third, therefore, the hypotheses are H0:P≥0.68 ; Ha:P0.68 Well done! You got it right.Let the parameter p be used to represent the proportion. The null hypothesis is always stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this case, the null hypothesis H0 is p≥0.68. The alternative hypothesis is contradictory to the null hypothesis, so Hais p0.68. Also, remember that the alternative hypothesis is the statement that the research or study is trying to show. In this case, they are trying to show that the politician is wrong, so the alternative hypothesis is the opposite of what the politician said. So Ha is p0.68. The null hypothesis is what the politician said, so H0 is p≥0.68. Differentiate between Type I and Type II errors when performing a hypothesis test Question Determine the Type II error if the null hypothesis, H0, is: a wooden ladder can withstand weights of 250pounds and less. ________________________________________ Select the correct answer below: ________________________________________ You think the ladder can withstand weight of 250 pounds and less when, in fact, it cannot. You think the ladder cannot withstand weight of 250 pounds and less when, in fact, it really can. You think the ladder can withstand weight of 250 pounds and less when, in fact, it can. You think the ladder cannot withstand weight of 250 pounds and less when, in fact, it cannot. Perfect. Your hard work is paying off Correct answer: You think the ladder can withstand weight of 250 pounds and less when, in fact, it cannot. A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is thinking the ladder can withstand weights of 250 pounds and less when, in fact, it cannot. Differentiate between Type I and Type II errors when performing a hypothesis test Question Determine the Type I error if the null hypothesis, H0, is: an electrician claims that no more than 10% of homes in the city are not up to the current electric codes. ________________________________________ Select the correct answer below: ________________________________________ The electrician thinks that no more than 10% of homes in the city are not up to the current electrical codes when, in fact, there really are no more than 10% that are not up to the current electric codes. The electrician thinks that more than 10% of the homes in the city are not up to the current electrical codes when, in fact, there really are more than 10% of the homes that do not meet the current electric codes. The electrician thinks that more than 10% of the homes in the city are not up to the current electrical codes when, in fact, at most 10% of the homes in the city are not up to the current electric codes. The electrician thinks that no more than 10% of homes in the city are not up to the current electrical codes when, in fact, more than 10% of the homes are not up to the current electric codes.Correct! You nailed it.A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when the electrician thinks that more than 10% of the homes are not up to code when, in fact, no more than 10%are not up to code. Identify the null and alternative hypotheses Question Which of the following results in a null hypothesis μ≤7 and alternative hypothesis μ7? ________________________________________ Select the correct answer below: ________________________________________ A study wants to show that the mean number of hours of sleep the average person gets each day is at least 7. A study wants to show that the mean number of hours of sleep the average person gets each day is 7. A study wants to show that the mean number of hours of sleep the average person gets each day is more than 7. A study wants to show that the mean number of hours of sleep the average person gets each day is at most 7.Yes that's right. Keep it up!Consider each of the options. The scenario in the third option has the null hypothesis μ≤7 based on the words "more than" and the fact that the null hypothesis is always stated with some form of equality. Also, remember that the alternative hypothesis is always the statement that is trying to be shown by the study. Distinguish between one- and two-tailed hypotheses tests and understand possible conclusions Question Identify the type of hypothesis test below. H0:X≥17.9, Ha:X17.9 ________________________________________ Select the correct answer below: ________________________________________ The hypothesis test is two-tailed. The hypothesis test is left-tailed. The hypothesis test is right-tailed. Yes that's right. Keep it up!Remember the forms of the hypothesis tests. • Right-tailed: H0:X≤X0, Ha:XX0. • Left-tailed: H0:X≥X0, Ha:XX0. • Two-tailed: H0:X=X0, Ha:X≠X0. So, this is a left-tailed test. Compute the value of the test statistic (z-value) for a hypothesis test for one population mean with a known standard deviation Question Annie, a long jumper, claims that her jump distance is not equal to 19 feet, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She makes 24 jumps. The mean distance of the sample jumps is 19.5 feet. Annie knows from experience that the standard deviation for her jump distance is 1.2 feet. • H0: μ=19; Ha: μ≠19 • α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? ________________________________________ Provide your answer below: ________________________________________ Test statistic = 2.04 This is one sample z-test - Hypothesis is Null H0:μ=19 Alternative Ha:μ̸=19 test statistic is - z=σ(Xˉ−μ)∗n Where Xˉ = sample mean Given than, Xˉ=19.5,μ=19,n=24,σ=1.2 using above value, test statistic (z) =2.04 Well done! You got it right.The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean distance, x¯=19.5. The sample the long jumper uses is 24 jumps, so n=24. She knows the standard deviation of the jumps, σ=1.2. Lastly, the long jumper is comparing the population mean distance to 19 feet. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=19.5−191.224√≈0.50.245≈2.04 So, the test statistic for this hypothesis test is z0=2.04. Differentiate between Type I and Type II errors when performing a hypothesis test Question A college administrator claims that the proportion of students that are nursing majors is greater than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 190 are nursing majors.The following is the setup for this hypothesis test: H0:p=0.40 Ha:p0.40 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve: z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 2.6 0.995 0.995 0.996 0.996 0.996 0.996 0.996 0.996 0.996 0.996 2.7 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 0.997 2.8 0.997 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.998 2.9 0.998 0.998 0.998 0.998 0.998 0.998 0.998 0.999 0.999 0.999 3.0 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 3.1 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 P-value=0.001 Required p-value = 0.001 Explanation: Formula to calculate the test statistic z is z=((1−p)∗p)/np^−p where p^=x/n=190/400=0.475,p=0.40,n=400 →((1−0.4)∗0.4)/4000.475−0.4 →0..075 ⇒3.06 P(z3.06) = 1-P(z3.06) ⇒ 1 - 0.999 [Find 3.0 in row and 0.06 in column in above table] ⇒ 0.001 Hence, p-value is 0.001Correct! You nailed it. Here are the steps needed to calculate the p-value for a hypothesis test for a proportion: 1. Determine if the hypothesis test is left tailed, right tailed, or two tailed. 2. Compute the value of the test statistic. 3. If the hypothesis test is left tailed, the p-value will be the area under the standard normal curve to the left of the test statistic z0 If the test is right tailed, the p-value will be the area under the standard normal curve to the right of the test statistic z0 If the test is two tailed, the p-value will be the area to the left of −|z0| plus the area to the right of |z0| under the standard normal curve For this example, the test is a right tailed test and the test statistic, rounding to two decimal places, is z=0.475−0.400.40(1−0.40)400‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√≈3.06. Thus the p-value is the area under the Standard Normal curve to the right of a z-score of 3.06.From a lookup table of the area under the Standard Normal curve, the corresponding area is then 1 - 0.999 = 0.001. Differentiate between Type I and Type II errors when performing a hypothesis test Question Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is the Type I error in this scenario? The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when the store thinks that less than 70% of its customers only shop at their sporting goods store when, in fact, it is at least 70%. ________________________________________ Perfect. Your hard work is paying off ________________________________________ Differentiate between Type I and Type II errors when performing a hypothesis test Question Determine the Type II error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt. Correct answer: The researchers think that 65% of college students will graduate with debt when, in fact, more or less than 65% of college students will graduate with debt. A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the researchers think that 65% of college students will graduate with debt when, in fact, more or less than 65% will graduate with debt. Identify the null and alternative hypotheses Question Which of the following results in a null hypothesis p≥0.44 and alternative hypothesis p0.44? Correct answer: An online article is trying to show that less than 44% of internet users participate in social media, contrary to an established figure saying that at least 44% of internet users participate in social media. Consider each of the options. Because the null hypothesis is p≥0.44, this must be the established fact that the article is trying to reject. The first answer choice is the correct choice, because the article is trying to show that less than 44% of users participate in social media (p0.44), which matches the alternative hypothesis given in the question. Your answer: An online article is trying to show that 44% of internet users participate in social media, contrary to an established figure saying that more than 44% of internet users participate in social media. dentify the null and alternative hypotheses Question A city wants to show that the mean number of public transportation users per day is more than 5,575. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. Correct answer: H0: μ≤5,575; Ha: μ5,575 Let the parameter μ be used to represent the mean. Remember that the null hypothesis is the statement already believed to be true, and the alternative hypothesis is the statement trying to be shown. In this case, the city is trying to show that μ5,575, so this is the alternative hypothesis. The null hypothesis is the opposite of this: μ≤5,575. Also, remember that the null hypothesis is always stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). So we can double check that this matches our answer above. Differentiate between Type I and Type II errors when performing a hypothesis test Question Determine the Type I error if the null hypothesis, H0, is: researchers claim that 65% of college students will graduate with debt. Correct answer: The researchers think that greater than or less than 65% of college students will graduate with debt when, in fact, 65% will graduate with debt. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when the researchers think that greater than or less than 65% of college students will graduate with debt when it actually will be 65%. Great work! That's correct. ________________________________________ Differentiate between Type I and Type II errors when performing a hypothesis test Question Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is β, the probability of a Type II error in this scenario? Perfect. Your hard work is paying off Correct answer: the probability that the sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% do not shop at any other sporting goods stores. Distinguish between one- and two-tailed hypotheses tests and understand possible conclusions Question Find the graph that matches the following hypothesis test. H0:X≥6.4, Ha:X6.4 Well done! You got it right. Distinguish between one- and two-tailed hypotheses tests and understand possible conclusions Question Which graph below corresponds to the following hypothesis test? H0:p≤8.1, Ha:p8.1 The alternative hypothesis, Ha, tells us which area of the graph we are interested in. Because the alternative hypothesis is p8.1, we are interested in the region greater than (to the right of) 8.1, so the correct graph is the second answer choice. Correct! You nailed it. Distinguish between one- and two-tailed hypotheses tests and understand possible conclusions Question Which graph below corresponds to the following hypothesis test? H0:μ≤16.9, Ha:μ16.9 Great work! That's correct.The alternative hypothesis, Ha, tells us which area of the graph we are interested in. Because the alternative hypothesis is μ16.9, we are interested in the region greater than (to the right of) 16.9, so the correct graph is the second answer choice. Compute the value of the test statistic (z-value) for a hypothesis test for one population mean with a known standard deviation Question Lexie, a bowler, claims that her bowling score is more than 140 points, on average. Several of her teammates do not believe her, so she decides to do a hypothesis test, at a 5% significance level, to persuade them. She bowls 18 games. The mean score of the sample games is 155 points. Lexie knows from experience that the standard deviation for her bowling score is 17 points. • H0: μ≤140; Ha: μ140 • α=0.05 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? ________________________________________ Perfect. Your hard work is paying off ________________________________________ Test statistic = 3.74The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean score, x¯=155. The sample the bowler uses is 18 games, so n=18. She knows the standard deviation of the games, σ=17. Lastly, the bowler is comparing the population mean score to 140 points. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=155−√≈154.007≈3.74 So, the test statistic for this hypothesis test is z0=3.74. Compute the value of the test statistic (z-value) for a hypothesis test for one population mean with a known standard deviation Question Suppose a pitcher claims that her pitch speed is not equal to 45 miles per hour, on average. Several of her teammates do not believe her, so the pitcher decides to do a hypothesis test, at a 1% significance level, to persuade them. She throws 21 pitches. The mean speed of the sample pitches is 46 miles per hour. The pitcher knows from experience that the standard deviation for her pitch speed is 6 miles per hour. • H0: μ=45; Ha: μ≠45 • α=0.01 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?Test statistic = 0.76The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean speed, x¯=46. The sample the pitcher uses is 21 pitches, so n=21. She knows the standard deviation of the pitches, σ=6. Lastly, the pitcher is comparing the population mean speed to 45 miles per hour. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=46−45621√≈11.309≈0.76 So, the test statistic for this hypothesis test is z0=0.76.