Question 1

A sports drink manufacturer claims that the mean finishing time for a marathon is $$1.67$$ hours. A sample of $$40$$ runners aged $$40$$–$$49$$ has a mean finishing time of $$1.62$$ hours and a standard deviation of $$0.25$$ hours. What is the standard error of the mean for this sample?

Accepted Answer

$$\frac{0.25}{\sqrt{40}}$$

Question 2

Which of the following best describes the sampling distribution of the sample mean?

Accepted Answer

It is the distribution of sample means from all possible samples of a given size.

Question 3

Suppose the probability that a sample mean is less than $$1.60$$ hours is $$4\%. $$What is the correct interpretation of this probability?

Accepted Answer

There is a $$4\%$$ chance that the sample mean of $$40$$ runners is less than $$1.60$$ hours.

Question 4

Which of the following is a parameter?

Accepted Answer

The mean finishing time of all marathon runners.

Question 5

A hypothesis test is performed to determine if the mean finishing time for the $$40$$–$$49$$ age group is significantly different from the population mean of $$1.67$$ hours. The sample mean is $$1.62$$ hours, the standard deviation is $$0.25$$ hours, and the sample size is $$40. $$What is the value of the test statistic?

Accepted Answer

$$z = \frac{1.62 - 1.67}{0.25/\sqrt{40}}$$

Question 6

If the $$95\%$$ confidence interval for the mean finishing time of the $$40$$–$$49$$ age group is $$(1.54, 1.77)$$ hours, what does this mean?

Accepted Answer

We are $$95\%$$ confident that the mean finishing time for the $$40$$–$$49$$ age group is between $$1.54$$ and $$1.77$$ hours.

Question 7

Which of the following is an example of a null hypothesis for an ANOVA test comparing mean GPAs across three different majors?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$ = \$$mu_3$

Question 8

Which of the following statements about the Central Limit Theorem (CLT) is correct?

Accepted Answer

The CLT states that the distribution of sample means approaches normality as the sample size increases.

Question 9

In an ANOVA test, what does a significant $$p-$$value indicate?

Accepted Answer

At least one group mean is different from the others.

Question 10

A researcher wants to test if there is an association between seating position and GPA. Which statistical test is most appropriate?

Accepted Answer

Chi-square test of independence

Question 11

Which of the following is an unbiased estimator of the population mean?

Accepted Answer

The sample mean $$\bar{x}$$

Question 12

If you increase the sample size in a study, what happens to the standard error of the mean?

Accepted Answer

It decreases.

Question 13

Which of the following is a correct interpretation of a $$p-$$value?

Accepted Answer

The probability of observing data as extreme as the sample, assuming the null hypothesis is true.

Question 14

A sample of $$50$$ randomly selected marathon runners has a mean finishing time of $$1.65$$ hours and a standard deviation of $$0.20$$ hours. Construct a $$95\%$$ confidence interval for the mean finishing time.

Accepted Answer

$$1.65 \pm 1.96 	imes \frac{0.20}{\sqrt{50}}$$

Question 15

Which of the following is NOT an assumption of ANOVA?

Accepted Answer

The population means are equal.

Question 16

If the $$p-$$value for a hypothesis test is $$0.019$$ and the significance level $$\alpha is$$ $$0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 17

Which of the following best describes a statistic?

Accepted Answer

A numerical summary calculated from a sample.

Question 18

A researcher performs a hypothesis test and obtains a $$z-$$score of $$-2.5. $$Which of the following is true?

Accepted Answer

The sample mean is $$2.5$$ standard errors below the population mean.

Question 19

Which of the following is the correct formula for the $$t-$$statistic in a one-sample $$t-$$test?

Accepted Answer

$$t = \frac{\bar{x} - \mu_0$}{s/\sqrt{n}}$$

Math 247 Exam 4 Review: Hypothesis Testing, Population Means, and ANOVA

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