Question 1

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

Accepted Answer

Rejecting a true null hypothesis

Question 2

A pharmaceutical company claims that at least 90% of patients recover after using its new drug. In a clinical trial, 180 out of 200 patients recovered. At a significance level of $$\alpha = 0.05$$, what is the correct null and alternative hypothesis for this test?

Accepted Answer

$$H_0$$: p = 0.90$$, H_1$: p \u003e 0.90$$

Question 3

In hypothesis testing, what does the p-value represent?

Accepted Answer

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true

Question 4

A researcher is testing whether the mean cholesterol level in a population is different from 200 mg/dL. Which of the following is the correct form of the alternative hypothesis for a two-tailed test?

Accepted Answer

$$H_1$$: \mu 
eq 200$$

Question 5

Suppose you are testing $$H_0$$: \mu = 50$$ versus H_1$: \mu \u003c 50$$ using a sample of $$n = 25$$, sample mean $$\bar{x} = 47$$, and sample standard deviation $$s = 5. $$What is the value of the test statistic?

Accepted Answer

$$t_0$$ = \dfrac{47 - 50}{5/\sqrt{25}} = -3.0$$

Question 6

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

Accepted Answer

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

Question 7

A left-tailed hypothesis test is being conducted at $$\alpha = 0.05. $$The calculated test statistic is $$z_0 = -2.1$. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis because $$z_0$$ falls in the critical region

Question 8

When testing a hypothesis about a population mean with a small sample size ($$n \u003c 30) $$and unknown population standard deviation, which distribution should be used?

Accepted Answer

Student's $$t-$$distribution

Question 9

A company claims that the standard deviation of the weights of its cereal boxes is 2 grams. A sample of 15 boxes has a sample standard deviation of 2.5 grams. Which test statistic should be used to test the company's claim?

Accepted Answer

$$\$$chi^2$$ = \dfrac{(n-1)s^2$}{\$$sigma_0$$^2}$$

Question 10

Which of the following best describes the difference between statistical significance and practical significance?

Accepted Answer

Statistical significance means the result is unlikely to occur by chance, while practical significance means the result is important in real life.

Question 11

A right-tailed hypothesis test for a population proportion is conducted at $$\alpha = 0.01. $$The calculated $$z-$$statistic is $$0.69. $$What is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis because $$z$$ does not fall in the critical region

Question 12

Which of the following is NOT a correct step in the traditional hypothesis testing procedure?

Accepted Answer

Calculate the p-value and compare it to the sample mean

Question 13

A sample of 224 patients is tested for a new drug, and 213 are healed. The manufacturer claims more than 94% are healed. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{213}{224} \approx 0.9509$$

Question 14

If the p-value for a hypothesis test is 0.2451 and $$\alpha = 0.01$$, what should you conclude?

Accepted Answer

Fail to reject the null hypothesis because the p-value is greater than $$\alpha$$

Question 15

Which of the following scenarios would require a one-tailed test?

Accepted Answer

Testing if the proportion is greater than a specific value

Question 16

A sample of 100 students who learned English and another language simultaneously had a mean SAT score of 485 with a standard deviation of 116. The population mean is 501. What is the value of the test statistic?

Accepted Answer

$$t_0$$ = \dfrac{485 - 501}{116/\sqrt{100}} = -1.38$$

Question 17

Which of the following is the correct formula for the test statistic when testing a population proportion?

Accepted Answer

$$z_0$$ = \dfrac{\hat{p} - $$p_0$$}{\sqrt{$$p_0(1$$-$$p_0)/n$$}}$$

Question 18

Which of the following is a possible outcome of a hypothesis test?

Accepted Answer

Fail to reject the null hypothesis

Question 19

In the context of hypothesis testing, what is a Type II error?

Accepted Answer

Failing to reject a false null hypothesis

Hypothesis Testing: Procedures for Proportions, Means, and Standard Deviations

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