Exam 10: Two-Sample Tests of Hypothesis

Of 150 adults who tried a new peach-flavoured peppermint patty, 87 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the 0.10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flavour as excellent? State the decision rule, the value of the test statistic, and your decision.

A random sample of 20 statistics students was given 15 multiple-choice questions and 15 open- ended questions-all on the same material. The professor was interested in determining which type of questions the students scored higher. This experiment is an example of

If two samples are used in a hypothesis test for which the combined degrees of freedom is 27, which one of the following might be true about the two sample sizes?

Married women are more often than not working outside the home on at least a part-time basis, as do most mannered men. Does a husband's employment status affect his wife's well being? In an attempt to answer this question, 75 married female professionals were surveyed as to their job satisfaction. In this sample, 45 husbands were employed, and 30 were unemployed. The Learning Objective of the study was to compare the mean job satisfaction levels of the married women with working husbands, with the mean job satisfaction levels of the married women with husbands that stayed at home. The test statistic for this problem has what type of distribution?

Of 150 adults who tried a new peach-flavoured peppermint patty, 99 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the 0.10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flavour as excellent? State the decision rule, the value of the test statistic, and your decision.

When is it appropriate to use the paired difference t-test?

Of 150 adults who tried a new peach-flavoured peppermint patty, 75 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the 0.10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flavour as excellent? State the decision rule, the value of the test statistic, and your decision.

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are presented below. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. This example is what type of test?

i. If samples taken from two populations are not independent, then a test of paired differences is applied. Ii) The paired difference test has (n1 + n2 - 2) degrees of freedom. Iii) The paired t test is especially appropriate when the sample sizes of two groups are the same.

i. We use the pooled estimate of the proportion in testing the difference between two population proportions. Ii) The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes. Iii) A committee studying employer-employee relations proposed that each employee would rate his or her immediate supervisor and in turn the supervisor would rate each employee. To find reactions regarding the proposal, 120 office personnel and 160 plant personnel were selected at random. Seventy-eight of the office personnel and 90 of the plant personnel were in favour of the proposal. Computed z = 1.48. At the 0.05 level, it was concluded that there is sufficient evidence to support the belief that the proportion of office personnel in favour of the proposal is greater than that of the plant personnel.

A local retail business wishes to determine if there is a difference in preferred indoor temperature between men and women. A random sample of data is collected, with the following results (note: there are slight differences between Excel and MegaStat output in this test): Using a 0.05 level of significance, can we conclude that there is indeed a difference in the temperature that men prefer compared to women? What is the null hypothesis if we assume men to be group 1 and women group 2?

The employees at the East Vancouver office of a multinational company are demanding higher salaries than those offered at the company office located in Oshawa Ontario. Their justification for the pay difference is that the difference between the average price of single-family houses in East Vancouver and that in Oshawa is more than $60,000. Before making a decision, the company management wants to study the difference in the prices of single-family houses for sale at the two locations. The results of their search of recent house sales are as follows (in $000, rounded to the nearest thousand): Assuming that the population distributions are approximately normal, can we conclude at the 0.05 significance level that the difference between the two population means is greater than $60,000? What is the alternate hypothesis?

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions? i. The null hypothesis is pa - pb = 0 ii. The alternate hypothesis is pa - pb ≠ 0 Iii) The proportion of sales made in Market Area 2 is 0.33.

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are presented below. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. What is the alternate hypothesis?

Which of the following conditions must be met to conduct a test for the difference in two sample means?

The results of a mathematics placement exam at Mercy College for two campuses are as follows: What is the computed value of the test statistic?

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? What is the null hypothesis?

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions? i. Using the 1% level of significance, the critical value is ±2.58. ii. The z-statistic is 3.57. Iii) Your decision is to reject the null hypothesis

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions? i. The null hypothesis is pa - pb = 0 Ii) The alternate hypothesis is pa - pb ≠ 0 Iii) The proportion of sales made in Market Area 1 is 0.45.

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are presented below. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. There are how many degrees of freedom?