Q: A researcher claims that the average monthly revenue per cell phone is different from $48.79. Which of the following is the correct set of hypotheses for this two-tailed test?

$$H_0$$: \mu = 48.79$$; H_a$$: \mu \neq 48.79$$

Q: A sample of 324 Chinese babies has a standard deviation of birth weights of $$50.4$$ grams. If the hypothesized population standard deviation is $$56.1$$ grams, what is the test statistic for testing the variance?

$$\$$chi^2$$ = \frac{(324-1) \times 50.4^2$}{56.1^2$}$$

Question 1

Which of the following best describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

A statement that there is no effect or no difference in the population.

Question 2

A researcher claims that the average monthly revenue per cell phone is different from $48.79. Which of the following is the correct set of hypotheses for this two-tailed test?

Accepted Answer

$$H_0$$: \mu = 48.79$$; H_a$$: \mu 
eq 48.79$$

Question 3

Which formula is used to calculate the test statistic for a population proportion?

Accepted Answer

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

Question 4

If a left-tailed test is being conducted at a significance level of $$\alpha = 0.05$$, what is the critical value for $$z$$?

Accepted Answer

$$z = -1.645$$

Question 5

A Type I error occurs when:

Accepted Answer

The null hypothesis is rejected when it is actually true.

Question 6

Given $$\bar{x} = 105$$, $$\mu = 100$$, $$s = 15$$, and $$n = 25$$, what is the $$t-$$statistic for testing the mean?

Accepted Answer

$$t = \frac{105 - 100}{\frac{15}{\sqrt{25}}} = \frac{5}{3} = 1.67$$

Question 7

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

Accepted Answer

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

Question 8

A sample of 324 Chinese babies has a standard deviation of birth weights of $$50.4$$ grams. If the hypothesized population standard deviation is $$56.1$$ grams, what is the test statistic for testing the variance?

Accepted Answer

$$\$$chi^2$$ = \frac{(324-1) 	imes 50.4^2$}{56.1^2$}$$

Question 9

In a right-tailed test, if the calculated $$z-$$statistic is $$2.33$$ and the critical value is $$1.96$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$ because $$z_{stat} is in $$the rejection region.

Question 10

Which of the following is NOT a requirement for testing a claim about a population mean using the $$t-$$test?

Accepted Answer

The population standard deviation must be known.

Question 11

A researcher wants to test if the standard deviation of supermodel heights is less than $$2.6$$ inches. Which is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \sigma = 2.6$$; H_a$$: \sigma \u003c 2.6$$

Question 12

If the $$p-$$value is $$0.019$$ and the significance level $$\alpha is$$ $$0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$ because $$p-$$value $$\u003c \alpha.$$

Question 13

Which of the following scenarios describes a Type II error?

Accepted Answer

Failing to reject the null hypothesis when the alternative hypothesis is actually true.

Question 14

A two-tailed test is being conducted with $$\alpha = 0.01. $$What is the critical value for $$z$$?

Accepted Answer

$$z = \pm 2.575$$

Question 15

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

Accepted Answer

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

Hypothesis Testing and Statistical Inference: Study Guide for Statistics Students

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