Question 1

A researcher wants to test the claim that the average caffeine content in a brand of energy drinks is greater than 80 mg. The population standard deviation is unknown, and the sample size is 25. Which distribution should the researcher use to conduct the hypothesis test?

Accepted Answer

t distribution

Question 2

Which of the following conditions must be met to use the normal z distribution for testing a claim about a mean?

Accepted Answer

The sample size $$n \u003e 30$$ and the population standard deviation $$\sigma is $$known.

Question 3

A sample of 40 smartphones has a mean radiation emission of 0.95 W/kg. Assume the population standard deviation $$\sigma = 0.20 W/kg. $$Test the claim at the 0.05 significance level that the mean emission is less than 1.00 W/kg. What is the value of the test statistic?

Accepted Answer

$$z = \dfrac{0.95 - 1.00}{0.20 / \sqrt{40}} = -1.58$$

Question 4

Suppose you are testing the claim that the mean systolic blood pressure of a population is 120 mmHg. You collect a sample of 16 patients, and the population standard deviation is unknown. Which method should you use to find the P-value?

Accepted Answer

Use the critical value method for the t distribution.

Question 5

A sample of 50 batteries has a mean lifetime of 98 hours. The population standard deviation is known to be 10 hours. Test the claim at the 0.01 significance level that the mean lifetime is different from 100 hours. What is the null hypothesis?

Accepted Answer

$$H_0$$: \mu = 100$$

Question 6

A nutritionist claims that the average sodium content in a brand of soup is less than 500 mg. A sample of 36 cans has a mean of 490 mg and a known population standard deviation of 30 mg. What is the appropriate test statistic formula?

Accepted Answer

$$z = \dfrac{490 - 500}{30 / \sqrt{36}}$$

Question 7

Which of the following statements is TRUE regarding the use of the t distribution for hypothesis testing about a mean?

Accepted Answer

The t distribution is used when the population standard deviation $$\sigma is $$unknown and the sample size is small.

Question 8

A company claims that their light bulbs last at least 1200 hours on average. A sample of 25 bulbs has a mean of 1180 hours and a sample standard deviation of 50 hours. At the 0.05 significance level, which test should be used?

Accepted Answer

A t-test for the mean

Question 9

If the sample size is large ($$n \u003e 30) $$and the population standard deviation is unknown, which distribution should be used to test a claim about the mean?

Accepted Answer

t distribution

Question 10

A sample of 20 patients has a mean cholesterol level of 190 mg/dL with a sample standard deviation of 15 mg/dL. The population is assumed normal. What is the formula for the test statistic to test if the mean is different from 200 mg/dL?

Accepted Answer

$$t = \dfrac{190 - 200}{15 / \sqrt{20}}$$

Question 11

A hospital administrator wants to test if the average wait time in the emergency room is more than 30 minutes. A sample of 45 patients has a mean wait time of 32 minutes and a known population standard deviation of 8 minutes. What is the alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003e 30$$

Question 12

Which of the following is a reason to use the critical value method instead of the P-value method when testing a claim about a mean with the t distribution?

Accepted Answer

Table A-3 does not provide P-values for the t distribution.

Question 13

A sample of 10 water samples has a mean lead concentration of 0.12 mg/L and a sample standard deviation of 0.03 mg/L. The population is assumed normal. What is the degrees of freedom for the t-test?

Accepted Answer

$$df = 9$$

Question 14

A pharmaceutical company wants to test if a new drug reduces average recovery time below 7 days. A sample of 36 patients has a mean recovery time of 6.5 days and a known population standard deviation of 1.2 days. What is the test statistic?

Accepted Answer

$$z = \dfrac{6.5 - 7}{1.2 / \sqrt{36}} = -2.5$$

Question 15

A sample of 15 students has a mean test score of 78 with a sample standard deviation of 5. The population is assumed normal. What is the correct formula for the test statistic to test if the mean is greater than 75?

Accepted Answer

$$t = \dfrac{78 - 75}{5 / \sqrt{15}}$$

Question 16

A sample of 100 apples has a mean weight of 150 grams. The population standard deviation is known to be 20 grams. What is the standard error of the mean?

Accepted Answer

$$\dfrac{20}{\sqrt{100}} = 2$$

Question 17

A researcher is testing the claim that the mean IQ score of a population is not equal to 100. Which of the following represents the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \mu 
eq 100$$

Question 18

A sample of 30 cars has a mean fuel efficiency of 25 mpg and a sample standard deviation of 4 mpg. The population is assumed normal. Which test should be used to determine if the mean differs from 27 mpg?

Accepted Answer

t-test for the mean

Question 19

A sample of 60 patients has a mean heart rate of 72 bpm. The population standard deviation is known to be 8 bpm. What is the formula for the test statistic to test if the mean is less than 75 bpm?

Accepted Answer

$$z = \dfrac{72 - 75}{8 / \sqrt{60}}$$

Hypothesis Testing for a Population Mean

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