Q: A researcher wants to test if the average cost of a hotel room in Chicago is different from $168. Which of the following is the correct set of hypotheses?

$$H_0$$: \mu = 168$$, H_1$: \mu \neq 168$$

Question 1

Which of the following best describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

It is a statement about a population parameter that represents the status quo.

Question 2

A researcher wants to test if the average cost of a hotel room in Chicago is different from $168. Which of the following is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \mu = 168$$, H_1$: \mu 
eq 168$$

Question 3

What is a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 4

If the significance level $$\alpha is $$decreased from 0.05 to 0.01, what happens to the probability of a Type II error ($$\beta$$), all else equal?

Accepted Answer

$$\beta$$ increases

Question 5

A company claims the mean monthly cell phone bill is at most $52. A manager believes it is higher. What are the correct hypotheses for this test?

Accepted Answer

$$H_0$$: \mu \leq 52$$, H_1$: \mu \u003e 52$$

Question 6

Which formula is used to calculate the test statistic for a hypothesis test about a mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$z = \frac{\bar{x} - \mu_0$}{\sigma / \sqrt{n}}$$

Question 7

In a two-tailed test with $$\alpha = 0.05$$, what are the critical z-values?

Accepted Answer

$$\pm 1.96$$

Question 8

A sample of 64 cell phone bills has a mean of $$53.1 and $$\sigma = 10$$. Test H_0$: \mu \leq 52 vs$$ $$H_1$$: \mu \u003e 52$$ at $$\alpha = 0.10$. What is the value of the test statistic?

Accepted Answer

$$z = 0.88$$

Question 9

What does the p-value represent in hypothesis testing?

Accepted Answer

The probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming $$H_0 is $$true.

Question 10

Which of the following increases the power of a hypothesis test?

Accepted Answer

Increasing the sample size ($$n)$$

Question 11

A two-tailed t-test is performed with $$n = 25$$, $$\bar{x} = 172.5$$, $$s = 15.4$$, $$\mu_0$ = 168$$, and $$\alpha = 0.05. $$What is the value of the test statistic?

Accepted Answer

$$t = 1.46$$

Question 12

Which of the following is true about the relationship between Type I and Type II errors?

Accepted Answer

If $$\alpha$$ increases, $$\beta$$ decreases, all else equal.

Question 13

Which of the following is NOT a possible outcome of a hypothesis test?

Accepted Answer

Accept $$H_1$$ when $$H_1 is $$true (Not a standard outcome)

Question 14

A researcher sets $$\alpha = 0.05$$ for a two-tailed test. The calculated p-value is 0.0456. What is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 15

Which formula is used to calculate the t statistic for a hypothesis test about a mean when the population standard deviation is unknown?

Accepted Answer

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

Question 16

In which scenario would you use a one-tailed test?

Accepted Answer

When the alternative hypothesis specifies a direction (e.g., $$H_1$$: \mu \u003e \$$mu_0)$$

Question 17

A sample mean is much larger than the hypothesized population mean. If the p-value is less than $$\alpha$$, what should you conclude?

Accepted Answer

Reject the null hypothesis

Hypothesis Testing: Single Population Mean and Proportion

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