Q: A company claims that the average time to deliver a package is 2 days. You want to test this claim using a sample of 30 deliveries. Which of the following correctly states the null and alternative hypotheses for a two-tailed test?

$H_0: \mu = 2$; $H_a: \mu \neq 2$

Q: You are testing the mean of a population with known standard deviation $\sigma$. Which test statistic should you use?

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

Q: A sample of 50 students has a mean test score of 78. The population standard deviation is known to be 10. What is the $z$-test statistic for testing $H_0: \mu = 75$?

$z = \frac{78 - 75}{10 / \sqrt{50}} = 2.12$

Q: If the p-value for a hypothesis test is 0.03 and the significance level $\alpha$ is 0.05, what should you conclude?

Reject the null hypothesis because $p$-value $< \alpha$

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

The probability of observing a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true

Q: A business wants to test if more than 40% of customers prefer online shopping. Which is the correct setup for the hypotheses?

$H_0: p \leq 0.40$; $H_a: p > 0.40$

Question 1

A company claims that the average time to deliver a package is 2 days. You want to test this claim using a sample of 30 deliveries. Which of the following correctly states the null and alternative hypotheses for a two-tailed test?

Accepted Answer

$H_0: \mu = 2$; $H_a: \mu 
eq 2$

Question 2

A medical researcher wants to test if the mean blood pressure in a population is less than 120 mmHg. Which is the correct setup for the hypotheses?

Accepted Answer

$H_0: \mu \geq 120$; $H_a: \mu < 120$

Question 3

You are testing the mean of a population with known standard deviation $\sigma$. Which test statistic should you use?

Accepted Answer

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

Question 4

A sample of 50 students has a mean test score of 78. The population standard deviation is known to be 10. What is the $z$-test statistic for testing $H_0: \mu = 75$?

Accepted Answer

$z = \frac{78 - 75}{10 / \sqrt{50}} = 2.12$

Question 5

If the p-value for a hypothesis test is 0.03 and the significance level $\alpha$ is 0.05, what should you conclude?

Accepted Answer

Reject the null hypothesis because $p$-value $< \alpha$

Question 6

Which of the following best describes the meaning of a p-value in hypothesis testing?

Accepted Answer

The probability of observing a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true

Question 7

A business wants to test if more than 40% of customers prefer online shopping. Which is the correct setup for the hypotheses?

Accepted Answer

$H_0: p \leq 0.40$; $H_a: p > 0.40$

Question 8

You collect a random sample of 100 customers and find that 48 prefer online shopping. What is the sample proportion $\hat{p}$?

Accepted Answer

$\hat{p} = \frac{48}{100} = 0.48$

Question 9

For testing a population proportion, which formula is used for the test statistic?

Accepted Answer

$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$

Question 10

A manufacturer claims that at least 95% of its products pass quality inspection. You take a sample of 200 products and find that 190 pass. What is the null hypothesis for a lower-tail test?

Accepted Answer

$H_0: p \geq 0.95$

Question 11

You are testing the mean of a population with unknown standard deviation. Which test statistic should you use?

Accepted Answer

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

Question 12

A sample of 25 employees has a mean salary of $55,000$ and sample standard deviation $s = 8,000$. What is the $t$-test statistic for testing $H_0: \mu = 50,000$?

Accepted Answer

$t = \frac{55,000 - 50,000}{8,000 / \sqrt{25}} = 3.125$

Question 13

Which of the following statements is TRUE regarding the critical value approach in hypothesis testing?

Accepted Answer

If the test statistic falls in the rejection region defined by the critical value, the null hypothesis is rejected

Question 14

A bank wants to test if the average waiting time is greater than 10 minutes. Which is the correct setup for the hypotheses?

Accepted Answer

$H_0: \mu \leq 10$; $H_a: \mu > 10$

Question 15

Which of the following is NOT a correct interpretation of a p-value?

Accepted Answer

The probability that the null hypothesis is true

Question 16

A retail store wants to test if the proportion of customers who use credit cards is different from 0.60. Which is the correct setup for the hypotheses?

Accepted Answer

$H_0: p = 0.60$; $H_a: p 
eq 0.60$

Question 17

You are given raw data for a sample and asked to test the mean of one population. Which of the following steps is NOT necessary?

Accepted Answer

Calculate the population mean $\mu$ from the sample

Question 18

A school administrator wants to test if the average test score is less than 70. A sample of 40 students has a mean of 68 and standard deviation of 6. What is the $t$-test statistic for $H_0: \mu = 70$?

Accepted Answer

$t = \frac{68 - 70}{6 / \sqrt{40}} = -2.11$

Chapter 9: Fundamentals of Hypothesis Testing – One-Sample Tests

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