Question 1

A hospital reported in 2015 that the mean years of experience among its nursing staff was 12 years. A nurse manager wants to test if the mean years of experience has increased. What is the correct null hypothesis ($$H_0) $$for this scenario?

Accepted Answer

$$H_0$$: \mu = 12$$

Question 2

Which of the following is the correct alternative hypothesis ($$H_a) to $$test if the mean years of experience among nurses has increased compared to 12 years?

Accepted Answer

$$H_a: \mu \u003e 12$$

Question 3

A nurse manager surveys 30 nurses and finds a sample mean of 15 years with a sample standard deviation of 10 years. What is the formula for the one-sample t-test statistic in this context?

Accepted Answer

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

Question 4

Given $$\bar{x} = 15$$, $$\mu_0$ = 12$$, $$s = 10$$, and $$n = 30$$, what is the calculated t-statistic? (Round to three decimal places.)

Accepted Answer

$$t = 1.643$$

Question 5

Why is a one-sample t-test appropriate for the nurse manager's study?

Accepted Answer

Because the sample mean is being compared to a known population mean and the population standard deviation is unknown.

Question 6

Suppose the critical t-value at $$\alpha = 0.05$$ with 29 degrees of freedom is 2.045. If the calculated t-statistic is 1.643, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not enough evidence the mean has increased.

Question 7

If the p-value associated with the t-statistic is 0.0181 and $$\alpha = 0.05$$, what does this indicate?

Accepted Answer

There is strong evidence to reject the null hypothesis in favor of the alternative.

Question 8

Which of the following best describes a Type I error in the context of this study?

Accepted Answer

Concluding the mean years of experience has increased when it actually has not.

Question 9

If the sample size were increased to 100 nurses, all else equal, what would happen to the standard error of the mean?

Accepted Answer

It would decrease.

Question 10

Which of the following is a correct interpretation of a p-value of 0.0181 in this context?

Accepted Answer

If the null hypothesis is true, there is a 1.81% probability of observing a sample mean at least as extreme as 15 years.

Question 11

Which assumption is NOT required for the validity of the one-sample t-test in this scenario?

Accepted Answer

The population standard deviation is known.

Question 12

If the sample mean had been 13 years instead of 15, with all other values unchanged, what would happen to the t-statistic?

Accepted Answer

It would decrease.

Question 13

What is the degrees of freedom used in the one-sample t-test for this study?

Accepted Answer

$$df = n - 1$$

Question 14

Which of the following would be an appropriate real-world conclusion if the p-value is less than 0.05?

Accepted Answer

There is sufficient evidence to conclude that the mean years of experience among nurses has increased since 2015.

Question 15

If the sample standard deviation was much larger, but the sample mean and size remained the same, what would happen to the t-statistic?

Accepted Answer

It would decrease.

Survey Sampling and Inference: Hypothesis Testing for Population Means (Chapter 7 Review)

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