MILESTONE
Sophia Introduction to Statistics Unit 5 – Milestone 5
(Below is a compilation of all questions for Unit 5 – Milestone 5. The answers are 100% correct, and it
guaranteed to earn you a perfect score in this unit. For a faster search, just hit on ctrl f on windows, or
command f on mac. Good luck!)
You passed this Milestone
24 questions were answered correctly.
1
Maximus is playing a game. When he rolls the dice he wins if he gets an even number
and loses if he gets an odd number.
Which of the following statements is FALSE?
• The count of rolling an odd number can be approximated with a normal distribution
• The count of rolling an even number can be approximated with a normal distribution
• Rolling an even number is considered a success
• The count of rolling an odd number from a sample proportion size of 100 can be
approximated with a normal distribution
RATIONALE
If we look at the counts from a large population of success and failures (2 outcomes),
this is called a binomial distribution. Since we are examining odds and evens, which
are discrete non-numeric values, the normal distribution cannot be used here.
CONCEPT
Distribution of Sample Proportions
2
Select the false statement about ANOVA.
• If a researcher wants to compare the mean wages of females in different age groups
at a particular company to the mean wages of males in different age groups at the
same company, the researcher should use a Two-Way ANOVA test.
• If a researcher wants to study the effectiveness of three brands of nicotine patches,
the researcher should use a One-Way ANOVA test.
• A one-way ANOVA hypothesis test considers comparisons between populations
based on one characteristic, while a two-way ANOVA hypothesis test considers
comparisons between populations based on multiple characteristics.
• If a researcher wants to compare the mean wages of females in different age groups
at a particular company, he or she should not use an ANOVA because the
population means are unknown.
RATIONALE
If performing a statistical test, we don't need to know the population values. This is
true for one-way ANOVA. We use the sample evidence to determine if the means
between groups in population are equal.
CONCEPT
One-Way ANOVA/Two-Way ANOVA
3
, Adam tabulated the values for the average speeds on each day of his road trip as 60.5,
63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309.
Select the 98% confidence interval for Adam’s set of data.
• 46.94 to 71.33
• 55.45 to 70.95
• 55.45 to 79.46
• 46.94 to 79.46
RATIONALE
In order to get the 98% CI , we first need to find the critical
t-score. Using a t-table, we need to find (n-1) degrees of freedom, or (8-1) = 7 df
and the corresponding CI.
Using the 98% CI in the bottom row and 7 df on the far left column, we get a t-critical
score of 2.998.
We also need to calculate the mean:
So we use the formula to find the confidence interval:
The lower bound is:
63.2-7.75 = 55.45
The upper bound is:
63.2+7.75 = 70.95
CONCEPT
Confidence Intervals Using the T-Distribution
4
Which of the following is an example of a parameter?
• Thirty randomly selected teens are asked about their average weekly hours spent on
the Internet.
• All 450 students attending a school are asked to rank the quality of cafeteria food.
• Over 10,000 out of 15,000 citizens in a precinct participate in a special election.
• Fifty students in first grade have their heights taken to estimate average length.
RATIONALE
Recall a parameter comes from the entire set of interest, the population. Since they
are looking at all students here, the ranking would be an example of a parameter.
CONCEPT
Sample Statistics and Population Parameters
5
, For a left-tailed test, the critical value of z so that a hypothesis test would reject
the null hypothesis at 1% significance level would be __________. Answer choices
are rounded to the hundredths place.
• -3.09
• -1.28
• -1.03
• -2.33
RATIONALE
Recall that when a test statistic is smaller than in a left tailed test we would reject H₀.
If we go to the standard normal chart and use 1% or 0.01, we will search for the
closest value to 1% as closely as possible.
0.0099 corresponds with a z-score of -2.33.
CONCEPT
How to Find a Critical Z Value
6
The government claims that the average age of Californians is 34 years. Joe
hypothesizes that the average age of the population of California is not equal to 34
years. He records a sample mean equal to 37 and states the hypothesis as μ = 34 vs μ ≠
34.
What type of test should Joe do?
• Two-tailed test
• Right-tailed test
• Left-tailed test
• Joe should not do any of the types of tests listed.
RATIONALE
Since the Hₐ is a not equal (≠) sign, this indicates he wants to run a two-tailed test
where the rejection region is the upper or lower tail.
CONCEPT
One-Tailed and Two-Tailed Tests
7
Sharon, an 8th grader, found the following values for weekly allowances in dollars of
seven of her friends: 5, 7, 10, 8, 6, 12, and 15.
If Sharon wanted to construct a one-sample t-statistic, what would the value for
the degrees of freedom be?
• 8
• 7
• 3
• 6
, RATIONALE
The degrees of freedom for a 1 sample t-test are df=n-1 where n is the sample
size. In this case, n=7, then df = n-1 = 7-1 = 6.
CONCEPT
T-Tests
8
Select the statement that correctly describes a Type I error.
• A Type I error occurs when the null hypothesis is accepted when it is actually false.
• A Type I error occurs when the null hypothesis is rejected when it is actually false.
• A Type I error occurs when the null hypothesis is accepted when it is actually true.
• A Type I error occurs when the null hypothesis is rejected when it is actually true.
RATIONALE
Recall a Type I error is when we incorrectly reject a true null hypothesis. So we
would reject H₀ using sample evidence, when in fact it was not true.
CONCEPT
Type I/II Errors
9
The table below shows the results of a customer satisfaction survey at a particular
restaurant broken down by males and females.
Male Female
Extremely Satisfied 25 7
Satisfied 21 13
Neutral 13 16
Dissatisfied 9 14
Extremely Dissatisfied 2 5
Assuming all 5 choices are equally likely, select the observed and expected
frequency for male customers that are dissatisfied.
• Observed: 14
Expected: 9
• Observed: 9
Expected: 14
• Observed: 9
Expected: 25
• Observed: 9
Expected: 12.5
RATIONALE
Sophia Introduction to Statistics Unit 5 – Milestone 5
(Below is a compilation of all questions for Unit 5 – Milestone 5. The answers are 100% correct, and it
guaranteed to earn you a perfect score in this unit. For a faster search, just hit on ctrl f on windows, or
command f on mac. Good luck!)
You passed this Milestone
24 questions were answered correctly.
1
Maximus is playing a game. When he rolls the dice he wins if he gets an even number
and loses if he gets an odd number.
Which of the following statements is FALSE?
• The count of rolling an odd number can be approximated with a normal distribution
• The count of rolling an even number can be approximated with a normal distribution
• Rolling an even number is considered a success
• The count of rolling an odd number from a sample proportion size of 100 can be
approximated with a normal distribution
RATIONALE
If we look at the counts from a large population of success and failures (2 outcomes),
this is called a binomial distribution. Since we are examining odds and evens, which
are discrete non-numeric values, the normal distribution cannot be used here.
CONCEPT
Distribution of Sample Proportions
2
Select the false statement about ANOVA.
• If a researcher wants to compare the mean wages of females in different age groups
at a particular company to the mean wages of males in different age groups at the
same company, the researcher should use a Two-Way ANOVA test.
• If a researcher wants to study the effectiveness of three brands of nicotine patches,
the researcher should use a One-Way ANOVA test.
• A one-way ANOVA hypothesis test considers comparisons between populations
based on one characteristic, while a two-way ANOVA hypothesis test considers
comparisons between populations based on multiple characteristics.
• If a researcher wants to compare the mean wages of females in different age groups
at a particular company, he or she should not use an ANOVA because the
population means are unknown.
RATIONALE
If performing a statistical test, we don't need to know the population values. This is
true for one-way ANOVA. We use the sample evidence to determine if the means
between groups in population are equal.
CONCEPT
One-Way ANOVA/Two-Way ANOVA
3
, Adam tabulated the values for the average speeds on each day of his road trip as 60.5,
63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309.
Select the 98% confidence interval for Adam’s set of data.
• 46.94 to 71.33
• 55.45 to 70.95
• 55.45 to 79.46
• 46.94 to 79.46
RATIONALE
In order to get the 98% CI , we first need to find the critical
t-score. Using a t-table, we need to find (n-1) degrees of freedom, or (8-1) = 7 df
and the corresponding CI.
Using the 98% CI in the bottom row and 7 df on the far left column, we get a t-critical
score of 2.998.
We also need to calculate the mean:
So we use the formula to find the confidence interval:
The lower bound is:
63.2-7.75 = 55.45
The upper bound is:
63.2+7.75 = 70.95
CONCEPT
Confidence Intervals Using the T-Distribution
4
Which of the following is an example of a parameter?
• Thirty randomly selected teens are asked about their average weekly hours spent on
the Internet.
• All 450 students attending a school are asked to rank the quality of cafeteria food.
• Over 10,000 out of 15,000 citizens in a precinct participate in a special election.
• Fifty students in first grade have their heights taken to estimate average length.
RATIONALE
Recall a parameter comes from the entire set of interest, the population. Since they
are looking at all students here, the ranking would be an example of a parameter.
CONCEPT
Sample Statistics and Population Parameters
5
, For a left-tailed test, the critical value of z so that a hypothesis test would reject
the null hypothesis at 1% significance level would be __________. Answer choices
are rounded to the hundredths place.
• -3.09
• -1.28
• -1.03
• -2.33
RATIONALE
Recall that when a test statistic is smaller than in a left tailed test we would reject H₀.
If we go to the standard normal chart and use 1% or 0.01, we will search for the
closest value to 1% as closely as possible.
0.0099 corresponds with a z-score of -2.33.
CONCEPT
How to Find a Critical Z Value
6
The government claims that the average age of Californians is 34 years. Joe
hypothesizes that the average age of the population of California is not equal to 34
years. He records a sample mean equal to 37 and states the hypothesis as μ = 34 vs μ ≠
34.
What type of test should Joe do?
• Two-tailed test
• Right-tailed test
• Left-tailed test
• Joe should not do any of the types of tests listed.
RATIONALE
Since the Hₐ is a not equal (≠) sign, this indicates he wants to run a two-tailed test
where the rejection region is the upper or lower tail.
CONCEPT
One-Tailed and Two-Tailed Tests
7
Sharon, an 8th grader, found the following values for weekly allowances in dollars of
seven of her friends: 5, 7, 10, 8, 6, 12, and 15.
If Sharon wanted to construct a one-sample t-statistic, what would the value for
the degrees of freedom be?
• 8
• 7
• 3
• 6
, RATIONALE
The degrees of freedom for a 1 sample t-test are df=n-1 where n is the sample
size. In this case, n=7, then df = n-1 = 7-1 = 6.
CONCEPT
T-Tests
8
Select the statement that correctly describes a Type I error.
• A Type I error occurs when the null hypothesis is accepted when it is actually false.
• A Type I error occurs when the null hypothesis is rejected when it is actually false.
• A Type I error occurs when the null hypothesis is accepted when it is actually true.
• A Type I error occurs when the null hypothesis is rejected when it is actually true.
RATIONALE
Recall a Type I error is when we incorrectly reject a true null hypothesis. So we
would reject H₀ using sample evidence, when in fact it was not true.
CONCEPT
Type I/II Errors
9
The table below shows the results of a customer satisfaction survey at a particular
restaurant broken down by males and females.
Male Female
Extremely Satisfied 25 7
Satisfied 21 13
Neutral 13 16
Dissatisfied 9 14
Extremely Dissatisfied 2 5
Assuming all 5 choices are equally likely, select the observed and expected
frequency for male customers that are dissatisfied.
• Observed: 14
Expected: 9
• Observed: 9
Expected: 14
• Observed: 9
Expected: 25
• Observed: 9
Expected: 12.5
RATIONALE
