MATH 302 Quiz 4 Question and Answers - Set 3| 2022 latest update | 100% correct

MATH 302 Quiz 4 Question and Answers - Set 3 Part 1 of 3 - 11.0/ 11.0 Points Question 1 of 20 1.0/ 1.0 Points If a teacher is trying to prove that a new method of teaching economics is more effective than a traditional one, he/she will conduct a: A.confidence interval B.one-tailed test C.two-tailed test D.point estimate of the population parameter Answer Key: B Question 2 of 20 1.0/ 1.0 Points In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7. At the  = .05 level of significance, does the nutritionist have enough evidence to reject the writer’s claim? A.Cannot Determine B.No C.Yes Answer Key: B Question 3 of 20 1.0/ 1.0 Points In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7. Compute the z or t value of the sample test statistic. A.z = 1.645 B.z = 1.916 C.t = 1.916 D.t = -1.916 Answer Key: C Question 4 of 20 1.0/ 1.0 Points Which of the following statements are true of the null and alternative hypotheses? A. Both hypotheses must be true B. It is possible for both hypotheses to be true C.Exactly one hypothesis must be true D.It is possible for neither hypothesis to be true Answer Key: C Question 5 of 20 1.0/ 1.0 Points Which of the following values is not typically used for ? A.0.50 B.0.10 C.0.01 D.0.05 Answer Key: A Question 6 of 20 1.0/ 1.0 Points A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy? State the null and alternative hypotheses. A.H0: 2 1.2, H1: 2 ≠ 1.2 B.H0: 2 ≠ 1.2, H1: 2 = 1.2 C.H0: 2 ≥ 1.2, H1: 2 ≠ 1.2 D.H0: 2 ≤ 1.2, H1: 2 1.2 Answer Key: D Question 7 of 20 1.0/ 1.0 Points Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 7.7 seconds. What would you use for the alternative hypothesis? A.H1: = 7.7 seconds B.H1: 7.7 seconds C.H1: 7.7 seconds D.H1: 7.7 seconds Answer Key: C Question 8 of 20 1.0/ 1.0 Points A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy? At the  = .01 level of significance, what is your conclusion? A.Cannot determine B. Reject H0. At the = .01 level of significance, there is not enough evidence to support the claim that this technician’s true variance is larger than the target accuracy. C.Do not reject H0. At the = .01 level of significance there is not sufficient evidence to suggest that this technician’s true variance is greater than the target accuracy. D.Reject H0. At the = .01 level of significance, there is enough evidence to support the claim that this technician’s variance is larger than the target accuracy. Answer Key: C Question 9 of 20 1.0/ 1.0 Points A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy? Compute the value of the appropriate test statistic. A. = 27.50 B. = 30.58 C.t = 27.50 D.z = 1.65 Answer Key: A Question 10 of 20 1.0/ 1.0 Points Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance. Compute the z or t value of the sample test statistic. A.t = 1.645 B.z = 0.69 C.z = 1.96 D.z = 0.62 Answer Key: B Question 11 of 20 1.0/ 1.0 Points A null hypothesis can only be rejected at the 5% significance level if and only if: A.a 95% confidence interval does not include the hypothesized value of the parameter B.the null hypotheses includes sampling error C.a 95% confidence interval includes the hypothesized value of the parameter D.the null hypothesis is biased Answer Key: A Part 2 of 3 - 2.0/ 6.0 Points Question 12 of 20 0.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. The ABC battery company claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company's claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below. Test of H0: 100 versus H1: 100 Sample mean 98.5 Std error of mean 0.777 Assuming the life length of batteries is normally distributed, if you wish to conduct this test using a .05 level of significance, what is the critical value that you should use? Place your answer, rounded to 3 decimal places in the blank. For example, -1.234 would be a legitimate entry. -1.930 Answer Key: -1.729 Question 13 of 20 0.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A medical doctor wishes to test the claim that the standard deviation of the systolic blood pressure of deep sea divers is greater than 450. To do so, she selected a random sample of 25 divers and found s = 468. Assuming that the systolic blood pressures of deep sea divers are normally distributed, the doctor would perform a chi-square test to test her research hypothesis. In that case, what is the test value that she would compute. Place your answer, rounded to 3 decimal places, in the blank. For example, 34.567 would be a legitimate entry. 42.980 Answer Key: 25.958 Question 14 of 20 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. The ABC battery company claims that their batteries last 100 hours, on average. You decide to conduct a test to see if the company's claim is true. You believe that the mean life may be different from the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below. Test of H0: = 100 versus H1: 100 Sample mean 98.5 Std error of mean 0.777 Assuming the life length of batteries is normally distributed, if you wish to conduct this test at the 0.05 level of significance, what are the critical values that you should use? Place the smaller critical value, rounded to 3 decimal places, in the first blank. For example, -1.234 would be a legitimate entry. -2.093 . Place the larger critical value, rounded to 3 decimal places, in the second blank. For example, 1.234 would be a legitimate entry. 2.093 Answer Key: -2.093, 2.093 Question 15 of 20 0.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A survey determines that mint chocolate chip is the favorite ice cream flavor of 6% of consumers. An ice cream shop determines that of 190 customers, 15 customers stated their preference for mint chocolate chip. Find the P-value that would be used to determine if the percentage of customers who prefer mint chocolate chip ice has increased at a 5% level of significance. P-value: 0.1251 Round your answer to four decimal places as necessary. Answer Key: 0.1357|0.1357 Feedback: This is a right-tail hypothesis test with a test statistic of z = 1.. Question 16 of 20 0.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. A firm that produces light bulbs claims that their lightbulbs last 1500 hours, on average. You wonder if the average might differ from the 1500 hours that the firm claims. To explore this possibility you take a random sample of n = 25 light bulbs purchased from this firm and record the lifetime (in hours) of each bulb. You then conduct an appopriate test of hypothesis. Some of the information related to the hypothesis test is presented below. Test of H0: = 1500 versus H1: 1500 Sample mean 1509.5 Sample Standard Deviation 24.27 Assuming the life length of this type of lightbulb is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.234 would be a legitimate entry. .031 Answer Key: 0.062 Question 17 of 20 1.0/ 1.0 Points Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker. Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values. For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. At a university, the average cost of books per student has been $550 per student per semester. The Dean of Students believes that the costs are increasing and that the average is now greater than $550. He surveys a sample of 40 students and finds that for the most recent semester their average cost was $630 with a standard deviation of $120. What is the test value for this hypothesis test? Test value: 4.22 Round your answer to two decimal places as necessary. Answer Key: 4.21|4.22 Part 3 of 3 - 2.0/ 3.0 Points Question 18 of 20 1.0/ 1.0 Points A one-tailed alternative is one that is supported by evidence in either direction. True False Answer Key: False Question 19 of 20 0.0/ 1.0 Points Sample evidence is statistically significant at the level only if the p–value is larger than . True False Answer Key: False Question 20 of 20 1.0/ 1.0 Points Using the confidence interval when conducting a two-tailed test for the population mean, we do not reject the null hypothesis if the hypothesized value for falls between the lower and upper confidence limits. True False Answer Key: True