Question 1

Which of the following is NOT a requirement for using the normal approximation method to test a claim about a population proportion?

Accepted Answer

The population standard deviation must be known.

Question 2

A researcher wants to test the claim that less than 30% of adults have sleepwalked. In a random sample of 19,136 adults, 29.2% reported sleepwalking. What is the correct null and alternative hypothesis for this test?

Accepted Answer

$$H_0$$: p = 0.30$$; H_1$: p \u003c 0.30$$

Question 3

Given a sample size $$n = 926$$ and sample proportion $$\hat{p} = 0.52$$, what is the correct formula to calculate the test statistic $$z$$ for testing $$H_0$$: p = 0.5$$?

Accepted Answer

$$z = \dfrac{0.52 - 0.5}{\sqrt{(0.5)(0.5)/926}}$$

Question 4

Why is it important to round the calculated number of successes $$x = n\hat{p} to a $$whole number when entering data into technology for hypothesis testing?

Accepted Answer

Because technology typically requires entry of a whole number for counts.

Question 5

Which statement best describes the relationship between the confidence interval method and the P-value/critical value methods when testing claims about proportions?

Accepted Answer

The confidence interval method uses the sample proportion for standard deviation, so it may lead to a different conclusion than the P-value and critical value methods.

Question 6

In the example testing whether most Internet users utilize two-factor authentication, the calculated P-value was 0.1056. If the significance level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

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

Question 7

Which formula is used to calculate the test statistic for testing a claim about a population mean when the population standard deviation is NOT known?

Accepted Answer

$$t = \dfrac{\bar{x} - \mu}{s/\sqrt{n}}$$

Question 8

A sample of $$n = 12$$ adults has a mean sleep time of $$\bar{x} = 6.83$$ hours and $$s = 1.99$$ hours. Test the claim that the mean sleep time is less than 7 hours. What is the value of the test statistic?

Accepted Answer

$$t = \dfrac{6.83 - 7}{1.99/\sqrt{12}} \approx -0.29$$

Question 9

When testing a claim about a population mean with unknown standard deviation, which distribution is used to find P-values and critical values?

Accepted Answer

Student $$t$$ distribution

Question 10

A sample of $$n = 106$$ body temperatures has $$\bar{x} = 98.20$$°F and $$s = 0.62$$°F. Test the claim that the population mean is 98.6°F. What is the correct test statistic?

Accepted Answer

$$t = \dfrac{98.20 - 98.6}{0.62/\sqrt{106}} \approx -6.61$$

Question 11

Which of the following is a requirement for testing a claim about a population standard deviation using the chi-square distribution?

Accepted Answer

The sample must be a simple random sample and the population must be normally distributed.

Question 12

What is the formula for the test statistic when testing a claim about a population variance $$\$$sigma^2$$?

Accepted Answer

$$\$$chi^2$$ = \dfrac{(n-1)s^2$}{\$$sigma^2$$}$$

Question 13

A mint claims its new process reduces the standard deviation of quarter weights below 0.062g. A sample of 24 quarters has $$s = 0.048g. $$What is the correct test statistic for this claim?

Accepted Answer

$$\$$chi^2$$ = \dfrac{(24-1)(0.048)^2$}{(0.062)^2$}$$

Question 14

Which property is TRUE about the chi-square ($$\$$chi^2$$) distribution?

Accepted Answer

It is not symmetric and all values are nonnegative.

Question 15

When using the exact method for testing claims about a proportion, what is the P-value for a left-tailed test?

Accepted Answer

P-value = $$P(x 	ext{ or fewer successes among } n 	ext{ trials})$$

Question 16

Which adjustment is made in the continuity correction for the exact method in hypothesis testing?

Accepted Answer

Subtract half the binomial probability at the boundary from the P-value.

Question 17

A confidence interval for the mean body temperature is $$98.08 \u003c \mu \u003c 98.32$$°F. The claim is $$\mu = 98.6$$°F. What does this interval suggest?

Accepted Answer

There is sufficient evidence to reject the claim that $$\mu = 98.6$$°F.

Hypothesis Testing: Testing a Claim about a Proportion (Chapter 8, Elementary Statistics)

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