Q: A sample of 500 students found that 219 scored at least 22 on the ACT math test. Test $$H_0$$: p = 0.5$$ vs H_1$: p \u003c 0.5 at$$ $$\alpha = 0.05. $$What is the value of the test statistic $$z_0$$?

$$z_0$$ = \frac{0.438 - 0.5}{\sqrt{\frac{0.5 \times 0.5}{500}}}$$

Question 1

A researcher wants to test if the mean lifetime of a new brand of light bulbs is less than 1000 hours. Which of the following correctly states the null and alternative hypotheses for this scenario?

Accepted Answer

$$H_0$$: \mu = 1000$$; H_1$: \mu \u003c 1000$$

Question 2

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 3

Suppose a pharmaceutical company claims that less than 5% of patients experience side effects from a new drug. A researcher tests $$H_0$$: p = 0.05$$ vs H_1$: p \u003c 0.05. If $$the researcher fails to reject $$H_0$$, what is the correct conclusion?

Accepted Answer

There is not sufficient evidence to conclude that less than 5% experience side effects.

Question 4

A Type II error occurs when:

Accepted Answer

We do not reject $$H_0$$ when $$H_1 is $$true.

Question 5

Which of the following statements about the significance level $$\alpha is $$correct?

Accepted Answer

$$\alpha is $$the probability of making a Type I error.

Question 6

A sample of 500 students found that 219 scored at least 22 on the ACT math test. Test $$H_0$$: p = 0.5$$ vs H_1$: p \u003c 0.5 at$$ $$\alpha = 0.05. $$What is the value of the test statistic $$z_0$$?

Accepted Answer

$$z_0$$ = \frac{0.438 - 0.5}{\sqrt{\frac{0.5 	imes 0.5}{500}}}$$

Question 7

If the P-value for a hypothesis test is 0.03 and $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 8

A 95% confidence interval for a population proportion is $$(0.28, 0.34). If $$the null hypothesis is $$H_0$$: p = 0.30$$, what is the correct conclusion?

Accepted Answer

Do not reject $$H_0$$ because 0.30 is in the interval.

Question 9

Which of the following is NOT an assumption for conducting a hypothesis test for a population mean?

Accepted Answer

The population standard deviation is known.

Question 10

A quality-control engineer tests if the mean weight of Snickers bars is different from 20.1 grams. He uses a sample of 11 bars and $$\alpha = 0.01. $$Which $$t-$$distribution critical value should he use for a two-tailed test?

Accepted Answer

$$t_{0.005, 10}$$

Question 11

Which of the following best describes practical significance?

Accepted Answer

A result that is statistically significant but not large enough to be important in practice.

Question 12

A left-tailed test is appropriate when:

Accepted Answer

The alternative hypothesis states the parameter is less than the null value.

Question 13

Which formula is used to calculate the test statistic for a population mean when the population standard deviation is unknown?

Accepted Answer

$$t_0$$ = \frac{\bar{x} - \$$mu_0$$}{s/\sqrt{n}}$$

Question 14

A survey finds that 353 out of 1200 teens text while driving. The null hypothesis is $$H_0$$: p = 0.34$$. Which is the correct formula for the standard error of the sample proportion?

Accepted Answer

$$SE = \sqrt{\frac{0.34 	imes 0.66}{1200}}$$

Question 15

If you want to find the critical value for a right-tailed $$t-$$test with 20 degrees of freedom and $$\alpha = 0.05$$, which value from the $$t-$$table should you use?

Accepted Answer

$$t_{0.05, 20}$$

Question 16

Which of the following is a correct interpretation of a P-value?

Accepted Answer

The probability of observing a sample statistic as extreme or more extreme than the one obtained, assuming the null hypothesis is true.

Question 17

A hypothesis test for a population mean yields a test statistic $$t_0 = 2.5$ with 15 degrees of freedom. For a right-tailed test at $$\alpha = 0.01$$, what is the correct decision if the critical value is t$$_{0.01, 15} = 2.602$$?

Accepted Answer

Fail to reject the null hypothesis.

Hypothesis Testing for One Sample: Proportion and Mean

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