Q: A company claims that the mean weight of its cereal boxes is 500g. A consumer group suspects the mean is different. Which is the correct set of hypotheses for a two-tailed test?

$H_0: \mu = 500,\ H_1: \mu \neq 500$

Q: Which formula is used to calculate the test statistic for a one-sample Z-test for the mean when the population standard deviation $\sigma$ is known?

$Z = \dfrac{\bar{X} - \mu}{\sigma / \sqrt{n}}$

Q: In a hypothesis test, what does the 'power' of a test represent?

The probability of rejecting $H_0$ when it is false.

Q: A sample of 25 hotels in New York has a mean price of $172.50 and a sample standard deviation of $15.40$. The hypothesized mean is $168$. What is the value of the t-statistic?

$t = \dfrac{172.50 - 168}{15.40 / \sqrt{25}} = 1.46$

Q: Which of the following is an assumption for using the t-test for the mean when $\sigma$ is unknown?

The population must be normally distributed or the sample size must be sufficiently large.

Q: A marketing company claims an 8% response rate. In a sample of 500, only 25 responses are received. What is the value of the Z-statistic for testing the proportion?

$Z = \dfrac{0.05 - 0.08}{\sqrt{0.08 \times 0.92 / 500}} = -2.47$

Q: Which of the following best describes the p-value in hypothesis testing?

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

Question 1

Which of the following statements about the null hypothesis ($H_0$) is TRUE?

Accepted Answer

It represents the current belief and is assumed true until evidence suggests otherwise.

Question 2

A company claims that the mean weight of its cereal boxes is 500g. A consumer group suspects the mean is different. Which is the correct set of hypotheses for a two-tailed test?

Accepted Answer

$H_0: \mu = 500,\ H_1: \mu 
eq 500$

Question 3

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 4

Suppose you conduct a hypothesis test at $\alpha = 0.01$ and obtain a p-value of 0.03. What is the correct decision?

Accepted Answer

Do not reject $H_0$ because the p-value is greater than $\alpha$.

Question 5

A researcher is testing whether the average commute time in a city is less than 30 minutes. Which is the correct alternative hypothesis?

Accepted Answer

$H_1: \mu < 30$

Question 6

Which formula is used to calculate the test statistic for a one-sample Z-test for the mean when the population standard deviation $\sigma$ is known?

Accepted Answer

$Z = \dfrac{\bar{X} - \mu}{\sigma / \sqrt{n}}$

Question 7

In a hypothesis test, what does the 'power' of a test represent?

Accepted Answer

The probability of rejecting $H_0$ when it is false.

Question 8

A sample of 25 hotels in New York has a mean price of $172.50 and a sample standard deviation of $15.40$. The hypothesized mean is $168$. What is the value of the t-statistic?

Accepted Answer

$t = \dfrac{172.50 - 168}{15.40 / \sqrt{25}} = 1.46$

Question 9

Which of the following is an assumption for using the t-test for the mean when $\sigma$ is unknown?

Accepted Answer

The population must be normally distributed or the sample size must be sufficiently large.

Question 10

A marketing company claims an 8% response rate. In a sample of 500, only 25 responses are received. What is the value of the Z-statistic for testing the proportion?

Accepted Answer

$Z = \dfrac{0.05 - 0.08}{\sqrt{0.08 	imes 0.92 / 500}} = -2.47$

Question 11

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

Accepted Answer

$\beta$ increases

Question 12

Which of the following best describes the p-value 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 13

A pharmaceutical company tests whether a new drug changes the average recovery time from a disease. The null hypothesis is $H_0: \mu = 10$ days. The 95% confidence interval for the mean recovery time is (9.2, 10.8). What is the correct conclusion at $\alpha = 0.05$?

Accepted Answer

Do not reject $H_0$ because 10 is in the interval.

Question 14

Which of the following is an example of an ethical issue in hypothesis testing?

Accepted Answer

Discarding data that does not support the researcher's hypothesis without justification.

Question 15

Which of the following factors will decrease the probability of a Type II error ($\beta$), all else equal?

Accepted Answer

Increasing the significance level ($\alpha$)

Question 16

A researcher is interested in whether the proportion of defective products is less than 5%. Which of the following is the correct null and alternative hypothesis?

Accepted Answer

$H_0: p = 0.05,\ H_1: p < 0.05$

Question 17

Which of the following statements about statistical significance and practical significance is TRUE?

Accepted Answer

A result can be statistically significant but not practically significant, especially with large sample sizes.

Question 18

A sample of 100 light bulbs has a mean life of 1200 hours. The population standard deviation is known to be 100 hours. The manufacturer claims the mean life is 1220 hours. What is the Z-statistic for testing the manufacturer's claim?

Accepted Answer

$Z = \dfrac{1200 - 1220}{100 / \sqrt{100}} = -2.0$

Question 19

Which of the following is NOT a step in the critical value approach to hypothesis testing?

Accepted Answer

Compute the p-value and compare it to $\alpha$.

Fundamentals of Hypothesis Testing: One-Sample Tests

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