Question 1

Which of the following is the correct formula for the test statistic when testing a claim about a population mean $$\mu$$ with unknown population standard deviation $$\sigma$$?

Accepted Answer

$$ t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}} $$

Question 2

A researcher wants to test the claim that the mean wait time for a ride is more than 30 minutes. The sample size is 40, the observed $$t$$ value is 0.940, the critical $$t$$ value is 1.685, and the significance level is 0.05. What is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; there is not sufficient evidence to support the claim.

Question 3

Which of the following is NOT a requirement for using the $$t-$$test for a population mean when $$\sigma is $$unknown?

Accepted Answer

The population standard deviation $$\sigma$$ must be known.

Question 4

A sample of 21 children with high lead exposure has a mean IQ of 86.90 and a standard deviation of 8.99. Test the claim that the population mean IQ is 100 at $$\alpha = 0.05. $$What is the null hypothesis?

Accepted Answer

$$ H_0$: \mu = 100 $$

Question 5

If the P-value for a hypothesis test is 0.177 and the significance level is 0.05, what should you conclude?

Accepted Answer

Fail to reject the null hypothesis.

Question 6

A sample of 8 cell phones has measured radiation levels (in W/kg) as follows: 0.97, 1.38, 0.93, 1.52, 1.37, 1.09, 0.48, 0.65. The FCC standard is 1.6 W/kg. What is the appropriate alternative hypothesis to test if the mean is less than the FCC standard?

Accepted Answer

$$ H_1$: \mu \u003c 1.6 $$

Question 7

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

Accepted Answer

The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

Question 8

In Example 4, the sample mean systolic blood pressure is 122.96 mm Hg, $$n = 300$$, $$s = 15.85$$, and the claim is that the mean is greater than 120 mm Hg. What is the correct test statistic formula to use?

Accepted Answer

$$ t = \frac{122.96 - 120}{\frac{15.85}{\sqrt{300}}} $$

Question 9

A hypothesis test results in a test statistic that does NOT fall in the critical region. What is the correct decision?

Accepted Answer

Fail to reject the null hypothesis.

Question 10

Which of the following scenarios would require the use of a $$t-$$distribution rather than a $$z-$$distribution?

Accepted Answer

The population standard deviation $$\sigma is $$unknown and the sample size is 25.

Question 11

A sample of 40 quarters has a test statistic $$t = -3.135$$ for testing $$H_0$$: \mu = 5.670$$ g at $$\alpha = 0.01$$. What does this result suggest?

Accepted Answer

There is sufficient evidence to reject the claim that the mean weight is 5.670 g.

Question 12

Which of the following is a valid interpretation of a 95% confidence interval for a population mean?

Accepted Answer

We are 95% confident that the interval contains the true population mean.

Question 13

If a sample does not appear to be from a normally distributed population and $$n \u003c 30$$, what should you do before conducting a $$t-$$test?

Accepted Answer

Consider using a nonparametric method such as the sign test or Wilcoxon signed-rank test.

Question 14

A sample of professional basketball player salaries is being tested for a mean greater than $$5$$ million dollars. The sample size is $$15$$ and the data are not normally distributed. What is the correct conclusion about the requirements for the $$t-$$test?

Accepted Answer

The requirements are not satisfied; the sample size is too small and the data are not normal.

Question 15

Which of the following best describes the critical value in a $$t-$$test?

Accepted Answer

The value that separates the critical region from the values that do not lead to rejection of $$H_0.$$

Step-by-Step Guidance for Hypothesis Testing About a Mean (σ Not Known)

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