Exam 10: Two-Sample Tests of Hypothesis

A recent study compared the time spent together by single and dual- earner couples. According to the records kept during the study, the mean amount of time spent together watching TV among single- earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean time was 48.4 and the standard deviation was 18.1. At a 0.01 significance level, can we conclude that the single-earner couples on average spend more time watching TV together? There were 15 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

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 alternate hypothesis is pa - pb ≠ 0 ii. The pooled estimate of the population proportion is 0.36. Iii) Using the 1% level of significance, the critical value is ±1.96.

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 critical t value at the 1% level of significance?

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. Given the following megastat printout, what analysis and decision can be made?

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 decision at the 1% level of significance?

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 alternate hypothesis is pa - pb ¹ 0 ii. The z-statistic is 3.57. iii. Your decision is to accept 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) If α = 0.01 and the z-statistic were calculated to be -1.96, your decision would be to fail to reject

Of 250 adults who tried a new multi-grain cereal, Wow!, 187 rated it excellent; of 100 children sampled, 66 rated it excellent. Using the 0.1 significance level and the alternate hypothesis p1 not equal to p2, what is the null hypothesis?

If two samples are used in a hypothesis test for which the combined degrees of freedom is 24, which one of the following CANNOT be true about the two sample sizes?

The results of a mathematics placement exam at Mercy College for two campuses are as follows: What is the null hypothesis if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?

10 and sample sizes of seven and fifteen, is ±1.734.

A poll of 400 people from village 1 showed 250 preferred chocolate raspberry coffee to the regular blend while 170 out of 350 in village 2 preferred the same flavour. To test the hypothesis that there is no difference in preferences in the two villages, what is the alternate hypothesis?

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 degree of freedom?

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): What is the degree of freedom?

Of 150 adults who tried a new peach-flavoured peppermint patty, 90 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.

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. If you were to use Excel's Data Analysis to assist in your solution to this problem, which test would you use?

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 value of calculated t?

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 degree of freedom?

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, 20 married female professionals were surveyed as to their job satisfaction. In this sample, 15 husbands were employed, and 5 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. Set up the hypotheses to test whether the job satisfaction levels of married women with working husbands is any more than that of their counterparts with unemployed husbands.

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on two samples, both sample sizes are 13?