Question 1

Which of the following is a requirement for testing a claim about a population mean when the population standard deviation $$\sigma is $$unknown?

Accepted Answer

The sample must be a simple random sample.

Question 2

When testing a claim about a mean with unknown $$\sigma$$, which distribution is used for the test statistic?

Accepted Answer

t-distribution

Question 3

Given a sample mean $$\bar{x} = 51$$, sample standard deviation $$s = 7$$, sample size $$n = 10$$, and a population mean claim $$\mu_0$ = 60$$, what is the value of the test statistic $$t$$?

Accepted Answer

$$t = \frac{51 - 60}{7/\sqrt{10}} = -4.08$$

Question 4

Which of the following statements about the t-distribution is FALSE?

Accepted Answer

The mean of a t-distribution is 1.

Question 5

A researcher wants to test if the mean pulse rate of students is different from 70 bpm. She collects a simple random sample of 35 students. Which method should she use to test her claim at $$\alpha = 0.05$$?

Accepted Answer

A t-test for the mean with unknown $$\sigma$$

Question 6

If a two-tailed t-test at $$\alpha = 0.05$$ yields a p-value of 0.1049, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis.

Question 7

Which of the following best describes the effect of increasing sample size on the t-distribution?

Accepted Answer

The t-distribution becomes closer to the normal distribution.

Question 8

A student estimates the length of one minute without a clock. The sample mean is 62 seconds, $$s = 8$$, $$n = 16. $$Test $$H_0$$: \mu = 60$$ vs H_1$: \mu 
eq 60 at$$ $$\alpha = 0.05. $$What is the test statistic?

Accepted Answer

$$t = \frac{62 - 60}{8/\sqrt{16}} = 1.0$$

Question 9

Which of the following is NOT a property of the t-distribution?

Accepted Answer

The t-distribution is used only for proportions.

Question 10

A confidence interval for a mean is calculated as $$(51.817, 73.455). If $$the claimed mean is 60, what is the correct interpretation?

Accepted Answer

There is not sufficient evidence to reject the claim that the population mean is 60.

Question 11

Which of the following scenarios would require the use of a two-tailed t-test?

Accepted Answer

Testing if the mean is different from a specific value.

Question 12

If the sample size is 25, sample mean is 4.1, sample standard deviation is 0.53, and the claimed population mean is 4.0, what is the value of the t-statistic?

Accepted Answer

$$t = \frac{4.1 - 4.0}{0.53/\sqrt{25}} = 0.943$$

Question 13

Why is the t-distribution used instead of the normal distribution when $$\sigma is $$unknown?

Accepted Answer

Because the sample standard deviation $$s is $$only an estimate of $$\sigma$$, introducing extra variability.

Question 14

A professor claims that the mean score on a final exam is 75. A sample of 36 students has a mean of 72 and a standard deviation of 9. What is the t-statistic for testing the professor's claim?

Accepted Answer

$$t = \frac{72 - 75}{9/\sqrt{36}} = -2.0$$

Question 15

Which of the following is a correct null hypothesis for testing if the mean time to complete a task is 30 minutes?

Accepted Answer

$$H_0$$: \mu = 30$$

Question 16

A sample of 20 patients has a mean recovery time of 8 days with a standard deviation of 2 days. The hospital claims the mean recovery time is 7 days. What is the t-statistic?

Accepted Answer

$$t = \frac{8 - 7}{2/\sqrt{20}} = 2.236$$

Question 17

If the p-value for a hypothesis test is less than the significance level $$\alpha$$, what should you do?

Accepted Answer

Reject the null hypothesis.

Question 18

Which of the following is a correct interpretation of a 95% confidence interval for a mean?

Accepted Answer

We are 95% confident that the true population mean lies within the interval.

Question 19

A sample of 15 measurements yields a mean of 10 and a standard deviation of 3. The claimed population mean is 12. What is the t-statistic?

Accepted Answer

$$t = \frac{10 - 12}{3/\sqrt{15}} = -2.58$$

Testing Claims about a Mean (Population Mean, $oldsymbol{ ext{μ}}$ Unknown)

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드

Testing Claims about a Mean (Population Mean, $oldsymbol{ ext{μ}}$ Unknown)

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드

Testing Claims about a Mean (Population Mean, $oldsymbol{ ext{μ}}$ Unknown)