Question 1

Which statement is not true about hypothesis tests?

Accepted Answer

Hypotheses in statistical tests are indeed statements about population parameters, not about the samples themselves. The purpose of using samples is to infer or make conclusions about the population from which they are drawn.

Question 2

The primary purpose of a significance test is to

Accepted Answer

The primary purpose of a significance test is to decide whether there is enough evidence to support a research hypothesis about a population, not just a sample. It uses sample data to make inferences about the population from which the sample was drawn.

Question 3

The level of significance associated with a significance test is the probability

Accepted Answer

The level of significance in hypothesis testing is the probability of rejecting a true null hypothesis, also known as the Type I error rate.

Question 4

A result is called statistically significant whenever

Accepted Answer

Statistical significance is determined when the p-value is less than or equal to the significance level, indicating that the observed data would be highly unlikely under the null hypothesis.

Question 5

Which of the following is not one of the steps for hypothesis testing?

Accepted Answer

The correct steps for hypothesis testing include determining the null and alternative hypotheses, verifying data conditions and calculating a test statistic, and assuming the null hypothesis is true to find the p-value. Assuming the alternative hypothesis is true to find the p-value is not a standard step in hypothesis testing. The focus is on the null hypothesis to determine the likelihood of observing the data if the null hypothesis were true.

Question 6

Which of the following is not a correct way to state a null hypothesis?

Accepted Answer

The null hypothesis should be a statement of no difference or no effect. Choice A is not a statement of no difference or no effect.

Question 7

In hypothesis testing for one mean, the "null value"is not used in which of the following?

Accepted Answer

The null value is not used in the computation of the (null) standard error; it is used in the null hypothesis, alternative hypothesis, and test statistic calculation.

Question 8

A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion?

Accepted Answer

The p-value of 0.02 indicates that there is only a 2% probability of observing a sample average of 71.8 or more extreme if the population average truly is 70. This low p-value typically leads to rejecting the null hypothesis that the population average is 70, as it suggests the observed difference is statistically significant.

Question 9

The p-value for a one-sided test for a mean was 0.04. The p-value for the corresponding two-sided test would be:

Accepted Answer

For a two-sided test, the p-value is doubled compared to a one-sided test because you are considering both tails of the distribution. Therefore, if the p-value for a one-sided test is 0.04, the p-value for the corresponding two-sided test would be 0.08.

Question 10

A null hypothesis is that the mean cholesterol level is 200 in a certain age group. The alternative is that the mean is not 200. Which of the following is the most significant evidence against the null and in favor of the alternative?

Accepted Answer

Larger sample sizes provide more reliable evidence against the null hypothesis. A sample size of 50 with a mean significantly different from 200 (180 in this case) offers stronger evidence against the null hypothesis than the other options.

Question 11

A test of H₀: $\mu$ = 0 versus H_a: $\mu$> 0 is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of $\alpha$ = 0.05. Which of the following will be the same for both researchers?

Accepted Answer

The power of the test depends on the sample size, significance level, and the true value of $\mu$, which are the same for both researchers.

Question 12

Which of the following is not true about hypothesis testing?

Accepted Answer

B) is incorrect because a relevant statistic is calculated from sample information, not population information, to form a test statistic. Hypothesis testing involves using sample data to make inferences about a population parameter.

Question 13

Use the following information for questions:
 An investigator wants to assess whether the mean $\mu$ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed.
-What are the appropriate null and alternative hypotheses?

Accepted Answer

The null hypothesis (H0) is typically a statement of no effect or no difference, so it would state that the mean weight $\mu$ equals the FAA guideline of 185 pounds. The alternative hypothesis (Ha) is what the investigator wants to assess or prove, which in this case is that the mean weight exceeds the guideline, hence $\mu > 185$.

Question 14

Use the following information for questions:
 An investigator wants to assess whether the mean $\mu$ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed.
-What is the value of the test statistic?

Accepted Answer

The test statistic is calculated using the formula: $ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} $, where $\bar{x} = 200$, $\mu = 185$, $s = 59.5$, and $n = 51$. Plugging in these values gives $ t = \frac{200 - 185}{59.5/\sqrt{51}} \approx 1.80 $.

Question 15

Use the following information for questions:
 An investigator wants to assess whether the mean $\mu$ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed.
-What is the p-value?

Accepted Answer

The test statistic is calculated using the formula for a one-sample t-test: $ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} $, where $\bar{x} = 200$, $\mu = 185$, $s = 59.5$, and $n = 51$. The calculated t-value is approximately 1.76. Using a t-distribution table or calculator with 50 degrees of freedom, the p-value for a one-tailed test is approximately 0.039.

Question 16

Use the following information for questions:
 An investigator wants to assess whether the mean $\mu$ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed.
-For a significance level of $\alpha$ = 0.05, are the results statistically significant?

Accepted Answer

The results are statistically significant because the sample mean (200 pounds) is significantly higher than the FAA guideline (185 pounds), and given the sample size, standard deviation, and significance level, it's likely that the p-value would be < 0.05, indicating statistical significance.

Question 17

Use the following information for questions:
 An investigator wants to assess whether the mean $\mu$ = the average weight of passengers flying on small planes exceeds the FAA guideline of average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed.
-Which of the following is an appropriate conclusion?

Accepted Answer

Given the sample mean is 200 pounds, which is greater than the FAA guideline of 185 pounds, and assuming the sample is representative and the calculations (not shown here) indicate statistical significance, it supports the conclusion that the average total weight of all passengers appears to be greater than 185 pounds.

Question 18

A random sample of 25 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. What is the value of the t-test statistic for determining if the mean score is significantly higher than 3?

Accepted Answer

The t-test statistic is calculated using the formula: t = (X̄ - μ) / (s/√n), where X̄ is the sample mean, μ is the population mean, s is the standard deviation, and n is the sample size. Plugging in the values: t = (3.2 - 3) / (0.95/√25) = 1.05.

Question 19

The WISC scores of a sample of n = 20 5^th graders resulted in a mean of 104 with a standard deviation of 9. Is the mean score significantly higher than 100 when $\alpha$ = 0.05?

Accepted Answer

The calculated t-value (1.99) is greater than the critical t-value (1.73) for a one-tailed test at $\alpha$ = 0.05 with 19 degrees of freedom, indicating the mean score is significantly higher than 100.

Question 20

A random sample of 25 third graders scored an average of 3.3 on a standardized spelling test. The standard deviation was 1.06. Is the mean score significantly higher than 3?

Accepted Answer

The answer of A random sample of 25 third graders...

Quiz 13: Testing Hypotheses About Means

Which statement is not true about hypothesis tests?

The primary purpose of a significance test is to

The level of significance associated with a significance test is the probability

A result is called statistically significant whenever

Which of the following is not one of the steps for hypothesis testing?

Which of the following is not a correct way to state a null hypothesis?

In hypothesis testing for one mean, the "null value"is not used in which of the following?

A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion?

The p-value for a one-sided test for a mean was 0.04. The p-value for the corresponding two-sided test would be:

A null hypothesis is that the mean cholesterol level is 200 in a certain age group. The alternative is that the mean is not 200. Which of the following is the most significant evidence against the null and in favor of the alternative?

A test of H₀: $\mu$ = 0 versus H_a: $\mu$ > 0 is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of $\alpha$ = 0.05. Which of the following will be the same for both researchers?

Which of the following is not true about hypothesis testing?

A random sample of 25 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. What is the value of the t-test statistic for determining if the mean score is significantly higher than 3?

The WISC scores of a sample of n = 20 5^th graders resulted in a mean of 104 with a standard deviation of 9. Is the mean score significantly higher than 100 when $\alpha$ = 0.05?

A random sample of 25 third graders scored an average of 3.3 on a standardized spelling test. The standard deviation was 1.06. Is the mean score significantly higher than 3?

Quiz 13: Testing Hypotheses About Means

Which statement is not true about hypothesis tests?

The primary purpose of a significance test is to

The level of significance associated with a significance test is the probability

A result is called statistically significant whenever

Which of the following is not one of the steps for hypothesis testing?

Which of the following is not a correct way to state a null hypothesis?

In hypothesis testing for one mean, the "null value"is not used in which of the following?

A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion?

The p-value for a one-sided test for a mean was 0.04. The p-value for the corresponding two-sided test would be:

A null hypothesis is that the mean cholesterol level is 200 in a certain age group. The alternative is that the mean is not 200. Which of the following is the most significant evidence against the null and in favor of the alternative?

A test of H0: μ\muμ = 0 versus Ha: μ\muμ > 0 is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of α\alphaα = 0.05. Which of the following will be the same for both researchers?

Which of the following is not true about hypothesis testing?

A random sample of 25 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. What is the value of the t-test statistic for determining if the mean score is significantly higher than 3?

The WISC scores of a sample of n = 20 5th graders resulted in a mean of 104 with a standard deviation of 9. Is the mean score significantly higher than 100 when α\alphaα = 0.05?

A random sample of 25 third graders scored an average of 3.3 on a standardized spelling test. The standard deviation was 1.06. Is the mean score significantly higher than 3?

A test of H₀: $\mu$ = 0 versus H_a: $\mu$ > 0 is conducted on the same population independently by two different researchers. They both use the same sample size and the same value of $\alpha$ = 0.05. Which of the following will be the same for both researchers?

The WISC scores of a sample of n = 20 5^th graders resulted in a mean of 104 with a standard deviation of 9. Is the mean score significantly higher than 100 when $\alpha$ = 0.05?