Question 1

Random samples of men and women have been given a scale that measures their support for gun control. Men average 10.2 with a standard deviation of 5.3. Women also average 10.2 but their standard deviation is 1.8. How could these results be dealt with appropriately?

Accepted Answer

The answer of Random samples of men and women have...

Question 2

Regarding importance versus statistics:________.

Accepted Answer

While statistics can assess significance, it is also important to consider the practical or theoretical significance of results. This can be done through various methods such as effect sizes, confidence intervals, and practical significance tests. Therefore, option A is correct. Option B is incorrect as researchers can formally assess importance through the aforementioned methods. Option C is incorrect as there is a clear difference between significance and importance. Finally, option D is incorrect as the distinction is not solely dependent upon data but also involves interpretation of results.

Question 3

A sample of students attending a large university has been selected. Is there a statistically significant difference between Liberal Arts majors and other students on average number of books (other than those required by course work) read per year? Use the five step model and write a sentence or two interpreting your results.

Accepted Answer

The answer of A sample of students attending a large...

Question 4

Samples of Republicans and Democrats have been tested for their level of support for a new immigration policy. The test statistic is 0.54 and the critical region begins at ± 1.96. What may we conclude?

Accepted Answer

The test statistic of 0.54 is not in the critical region (± 1.96) which means that we fail to reject the null hypothesis that there is no significant difference between the level of support for the new immigration policy among Republicans and Democrats. Therefore, we can conclude that the difference is not significant.

Question 5

To satisfy the requirement of independent random sampling, the researcher________.

Accepted Answer

Randomly selecting cases from one list of the population and subdividing the sample according to the trait of interest allows for independent random sampling, as long as the initial list is randomly generated or representative of the population. Other options such as cluster sampling or selecting entire neighborhoods do not guarantee independent random sampling. The option of selecting very small populations may also not ensure independent random sampling.

Question 6

Samples of Republicans and Democrats have been tested for their level of support for welfare reform and the null hypothesis has been rejected. What may we conclude?

Accepted Answer

The rejection of the null hypothesis means that there is a significant difference between the two groups. Therefore, we can conclude that there are differences between Republicans and Democrats on the issue of welfare reform.

Question 7

Very large random samples of Catholics and Protestants have been questioned about their opinions on cohabitation. Forty-six percent of the Protestant and 47% of the Catholics approve of males and females living together without being married. The difference has been tested and found to be statistically significant. What is the most reasonable conclusion?

Accepted Answer

The difference between 46% and 47% is very small, so even though it is statistically significant due to the large sample sizes, the practical importance of this difference is minimal. Statistical significance does not always imply practical significance.

Question 8

To maximize the probability of rejecting the null hypothesis, use________.

Accepted Answer

To maximize the probability of rejecting the null hypothesis, we need to choose a higher alpha level, a large sample size, and a one-tailed test as it has a smaller critical value and thereby increasing the chance of rejecting the null hypothesis. A low alpha level and a two-tailed test will reduce the chance of rejecting the null hypothesis. Choosing low alphas and high Z scores are not necessarily connected to maximizing the probability of rejecting the null hypothesis. High alphas but low degrees of freedom would not give a reliable result for the statistical test.

Question 9

In the two sample case, the null hypothesis is always about the difference in the________.

Accepted Answer

The null hypothesis in the two sample case is always about the difference in the populations. This is because we are comparing two separate groups and trying to determine if there is a significant difference between them, which would suggest that the populations they come from are also different. The other answer choices are not relevant to the null hypothesis in this case.

Question 10

The text reports the results of a test for the significance of the difference in average income for random samples of males and females. Males earned an average of about $17,000 more per year and the Z score computed in step 4 was 6.28. Given these results, which of the following is a reasonable conclusion?

Accepted Answer

A Z score of 6.28 indicates a very large difference between the two groups, and the fact that the difference is statistically significant suggests that it is not due to chance alone. Therefore, it is reasonable to conclude that the difference in average income between males and females is not only statistically significant but also large and important.

Question 11

A scale measuring confidence in the media was administered to a sample. Is there a statistically significant difference between Democrats and Republicans on the scale? Higher scores on the scale indicate greater confidence. Use the five step model and write a sentence or two interpreting your results.

Accepted Answer

The answer of A scale measuring confidence in the media...

Question 12

When researchers present their findings using a two-sample hypothesis test, they usually include all but which of the following:________.

Accepted Answer

The critical region is not usually included in the presentation of findings as it is a predetermined level of significance used to reject or fail to reject the null hypothesis. It is not specific to the study or the sample data.

Question 13

Rejection of the null hypothesis in the two-sample case implies that the________.

Accepted Answer

Rejection of the null hypothesis in the two-sample case implies that there is enough evidence to suggest that the populations from which the samples are drawn are different on the trait of interest. Therefore, choice B is the best choice.

Question 14

When conducting hypothesis tests for two sample means, the term μ 1- μ 2in the numerator of the formula reduces to zero because________.

Accepted Answer

The numerator of the formula (μ 1- μ 2) represents the difference between the population means of the two groups being compared. In hypothesis testing, the null hypothesis assumes that there is no significant difference between the two population means. Therefore, when conducting hypothesis tests for two sample means, the null hypothesis is assumed to be true, which means that there is no significant difference between the population means. As a result, the difference between the two population means in the numerator of the formula reduces to zero, so D is the correct answer.

Question 15

A pooled estimate________.

Accepted Answer

A pooled estimate combines information from two samples, typically two groups of data collected under different conditions or from different populations. It is used to estimate a common population parameter such as the population mean or variance. Comparing populations, combining populations, or taking the mean of standard deviations are not part of the definition of a pooled estimate.

Question 16

The text reports the results of a test for the significance of the difference in average education for random samples of males and females. Both males and females averaged 13.5 years of schooling. The Z score computed in step 4 for this difference was - 0.29. Given these results, which of the following is a reasonable conclusion?

Accepted Answer

The Z score of -0.29 indicates that the difference in average education between males and females is not statistically significant at the 0.05 level of significance. Therefore, it is likely that the difference is due to random chance and not a meaningful gender gap in education.

Question 17

According to information supplied by the U.S. Bureau of the Census, between 1955 and 2005, the gender gap in income closed from________.

Accepted Answer

According to the information, the gender gap in income closed from 64% to 79% between 1955 and 2005.

Quiz 9: Hypothesis Testing Ii the Two Sample Case