Question 1

In making the decision to reject the null hypothesis, what would happen if you were to change α from .05 to .01?

Accepted Answer

Lowering α from .05 to .01 decreases the probability of making a Type I error (falsely rejecting the null hypothesis), making it more stringent and thus less likely to reject the null hypothesis unless the evidence against it is stronger.

Question 2

Which of the following null hypotheses would result in calculating the t-test for a single mean?

Accepted Answer

The null hypothesis for a t-test for a single mean is always about a population mean being equal to a specific value (μ = a). Choice A is a null hypothesis for a one-tailed t-test for a population mean being greater than a specific value. Choice B is a null hypothesis for an independent t-test for comparing means of two groups. Choice C is a null hypothesis for a two-sample t-test for comparing means of two groups.

Question 3

For a t-statistic = 3.20 with 10 degrees of freedom, what would be the appropriate statement about the significance level?

Accepted Answer

With 10 degrees of freedom, the critical value for a two-tailed test at the 0.01 level of significance is +/-3.169. Since the calculated t-statistic of 3.20 is greater than the critical value, we reject the null hypothesis and conclude that the result is statistically significant at the p < 0.01 level.

Question 4

What did the researcher do to cause the change in the shaded regions from Distribution A to Distribution B?  Distribution A  Distribution B

Accepted Answer

The answer of What did the researcher do to cause...

Question 5

The larger the ______, the ______ likely you are to reject the null hypothesis.

Accepted Answer

The value for alpha represents the level of statistical significance chosen for a given test. If the value for alpha is larger, it means that the researcher is willing to tolerate a greater likelihood of rejecting the null hypothesis when it is actually true. Therefore, the larger the value for alpha, the more likely the researcher is to reject the null hypothesis.

Question 6

What did the researcher do to cause the change in the shaded regions in the two distributions?  "Before"  "After"

Accepted Answer

The answer of What did the researcher do to cause...

Question 7

What happens when you change α from .05 to .10?

Accepted Answer

When you increase α from .05 to .10, the critical value(s) decrease, making the criteria for rejecting the null hypothesis less stringent. This means the threshold for what is considered statistically significant is lowered.

Question 8

A researcher conducts a study measuring 20 children before and after they play violent video games and obtains a value of 1.98 for the t-statistic. For a non-directional alternative hypothesis, which of the following is the correct way to present this analysis?

Accepted Answer

Since the researcher is measuring the same group of children before and after playing violent video games, this is a paired-samples t-test. Therefore, the degrees of freedom are n-1, where n=20, resulting in 19 degrees of freedom. Additionally, the t-statistic of 1.98 falls above the critical value of 2.093 for a two-tailed test with 19 degrees of freedom at alpha level .05. Therefore, the p-value must be greater than .05. Therefore, the correct way to present this analysis is: t(19) = 1.98, p > .05.

Question 9

Holding all else constant, the larger the sample size, the ______ the standard error of the difference  and the ______ the value of the t-statistic (t).

Accepted Answer

The answer of Holding all else constant, the larger the...

Question 10

Bill and Bob conduct two separate studies. By an amazing coincidence, they obtain exactly the same sample means and standard deviations. However, Bill's sample is twice as large as Bob's. Which of these is true?

Accepted Answer

Bill's larger sample size gives him more statistical power, making it more likely for him to reject the null hypothesis if there is indeed an effect.

Question 11

In making the decision to reject H₀, what happens if you set α at .10 rather than .05?

Accepted Answer

When α is set at .10 instead of .05, the region of rejection gets bigger. This means that the threshold for rejecting the null hypothesis is lower, so it is more likely that we will reject the null hypothesis.

Question 12

Mary and Joe conduct two separate studies. By an amazing coincidence, they obtain exactly the same sample means and standard deviations. However, Mary's sample is twice as large as Joe's. Which of these is true?

Accepted Answer

Mary's larger sample size means her study has a lower standard error, leading to smaller critical values for the same level of significance compared to Joe's study with a smaller sample size.

Question 13

A college professor was interested in comparing the average starting salaries of Engineering and English majors. Which type of statistical analysis should she use to analyze this data?

Accepted Answer

The professor is comparing the salaries of two different groups (Engineering and English majors), so she should use a t-test for independent means.

Question 14

In which of the following situations would you MOST likely use the t-test for dependent means?

Accepted Answer

The t-test for dependent means is used when comparing the means of two related or paired samples, such as comparing stress levels before and after a yoga class for the same group of people. Option A involves comparing means of two independent groups, option C involves comparing means of vastly different groups, and option D involves comparing a sample mean to a population mean without a paired sample.

Question 15

What did the researcher do to cause the change in the shaded regions in the two distributions?  "Before"  "After"

Accepted Answer

The answer of What did the researcher do to cause...

Question 16

A researcher conducts a study measuring 10 people before and after they watch a movie and obtains a value of 2.85 for the t-statistic. For a non-directional alternative hypothesis, which of the following is the correct way to present this analysis?

Accepted Answer

In a study where measurements are taken before and after an intervention on the same subjects, the degrees of freedom (df) for a paired samples t-test is calculated as the number of pairs minus one. Since there are 10 people (10 pairs of before and after measurements), the degrees of freedom is 10 - 1 = 9, making the correct presentation of the t-statistic t(9) = 2.85. The p-value is typically determined by the context of the t-distribution and the calculated t-statistic, but without specific p-value thresholds given, p < .05 is a common significance level used in social sciences, making option B the correct choice.

Question 17

The smaller the ______, the ______ likely you are to reject the null hypothesis.

Accepted Answer

A smaller value for alpha means a stricter criterion for rejecting the null hypothesis, making it less likely to reject it.

Question 18

Holding all else constant, as sample sizes increase, the degrees of freedom ______ and the critical value(s) ______.

Accepted Answer

As sample sizes increase, the degrees of freedom (which are typically calculated based on sample size, such as n-1 for a single sample) also increase. Larger sample sizes generally lead to more precise estimates, allowing for narrower confidence intervals, which means the critical values (thresholds for statistical significance) decrease.

Question 19

A marriage counselor wishing to compare the values of married couples collects data from 10 husbands and their wives. Which type of statistical analysis should she use to analyze this data?

Accepted Answer

A t-test for dependent means is appropriate for comparing two related samples, such as scores from the same individuals (in this case, husbands and their wives) before and after a treatment or in a matched-pairs situation. Since the data comes from married couples, their scores are naturally paired, making this the correct choice.

Question 20

In which of the following situations would you MOST likely use the t-test for independent means?

Accepted Answer

The t-test for independent means is used when comparing two groups that are not related to each other, such as BMW and Saturn car owners.

Quiz 9: Testing the Difference Between Two Means

In making the decision to reject the null hypothesis, what would happen if you were to change α from .05 to .01?

Which of the following null hypotheses would result in calculating the t-test for a single mean?

For a t-statistic = 3.20 with 10 degrees of freedom, what would be the appropriate statement about the significance level?

What did the researcher do to cause the change in the shaded regions from Distribution A to Distribution B? Distribution A Distribution B

The larger the , the likely you are to reject the null hypothesis.

What did the researcher do to cause the change in the shaded regions in the two distributions? "Before" "After"

What happens when you change α from .05 to .10?

A researcher conducts a study measuring 20 children before and after they play violent video games and obtains a value of 1.98 for the t-statistic. For a non-directional alternative hypothesis, which of the following is the correct way to present this analysis?

Holding all else constant, the larger the sample size, the the standard error of the difference and the the value of the t-statistic (t) .

Bill and Bob conduct two separate studies. By an amazing coincidence, they obtain exactly the same sample means and standard deviations. However, Bill's sample is twice as large as Bob's. Which of these is true?

In making the decision to reject H₀, what happens if you set α at .10 rather than .05?

Mary and Joe conduct two separate studies. By an amazing coincidence, they obtain exactly the same sample means and standard deviations. However, Mary's sample is twice as large as Joe's. Which of these is true?

A college professor was interested in comparing the average starting salaries of Engineering and English majors. Which type of statistical analysis should she use to analyze this data?

In which of the following situations would you MOST likely use the t-test for dependent means?

What did the researcher do to cause the change in the shaded regions in the two distributions? "Before" "After"

A researcher conducts a study measuring 10 people before and after they watch a movie and obtains a value of 2.85 for the t-statistic. For a non-directional alternative hypothesis, which of the following is the correct way to present this analysis?

The smaller the , the likely you are to reject the null hypothesis.

Holding all else constant, as sample sizes increase, the degrees of freedom and the critical value(s) .

A marriage counselor wishing to compare the values of married couples collects data from 10 husbands and their wives. Which type of statistical analysis should she use to analyze this data?

In which of the following situations would you MOST likely use the t-test for independent means?

Quiz 9: Testing the Difference Between Two Means

In making the decision to reject the null hypothesis, what would happen if you were to change α from .05 to .01?

Which of the following null hypotheses would result in calculating the t-test for a single mean?

For a t-statistic = 3.20 with 10 degrees of freedom, what would be the appropriate statement about the significance level?

What did the researcher do to cause the change in the shaded regions from Distribution A to Distribution B? Distribution A Distribution B

The larger the ______, the ______ likely you are to reject the null hypothesis.

What did the researcher do to cause the change in the shaded regions in the two distributions? "Before" "After"

What happens when you change α from .05 to .10?

A researcher conducts a study measuring 20 children before and after they play violent video games and obtains a value of 1.98 for the t-statistic. For a non-directional alternative hypothesis, which of the following is the correct way to present this analysis?

Holding all else constant, the larger the sample size, the ______ the standard error of the difference and the ______ the value of the t-statistic (t) .

Bill and Bob conduct two separate studies. By an amazing coincidence, they obtain exactly the same sample means and standard deviations. However, Bill's sample is twice as large as Bob's. Which of these is true?

In making the decision to reject H0, what happens if you set α at .10 rather than .05?

Mary and Joe conduct two separate studies. By an amazing coincidence, they obtain exactly the same sample means and standard deviations. However, Mary's sample is twice as large as Joe's. Which of these is true?

A college professor was interested in comparing the average starting salaries of Engineering and English majors. Which type of statistical analysis should she use to analyze this data?

In which of the following situations would you MOST likely use the t-test for dependent means?

What did the researcher do to cause the change in the shaded regions in the two distributions? "Before" "After"

A researcher conducts a study measuring 10 people before and after they watch a movie and obtains a value of 2.85 for the t-statistic. For a non-directional alternative hypothesis, which of the following is the correct way to present this analysis?

The smaller the ______, the ______ likely you are to reject the null hypothesis.

Holding all else constant, as sample sizes increase, the degrees of freedom ______ and the critical value(s) ______.

A marriage counselor wishing to compare the values of married couples collects data from 10 husbands and their wives. Which type of statistical analysis should she use to analyze this data?

In which of the following situations would you MOST likely use the t-test for independent means?

The larger the , the likely you are to reject the null hypothesis.

Holding all else constant, the larger the sample size, the the standard error of the difference and the the value of the t-statistic (t) .

In making the decision to reject H₀, what happens if you set α at .10 rather than .05?

The smaller the , the likely you are to reject the null hypothesis.

Holding all else constant, as sample sizes increase, the degrees of freedom and the critical value(s) .