Exam 10: Two-Sample Tests of 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 $1000) 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 decision at the 5% 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 null hypothesis is p_a - p_b = 0. ii. The alternate hypothesis is p_a - p_b $\neq$ 0. iii. The proportion of sales made in Market Area 2 is 0.33.

i. The paired difference test has (n₁ + n₂ - 2) degrees of freedom. ii. The paired t test is especially appropriate when the sample sizes of two groups are the same. iii. A statistics professor wants to compare grades of two different groups of students taking the same course in two different sections. This is an example of a paired sample.

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 $1000) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? This example is what type of test?

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.

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 65 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.

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow: If the calculated test statistic is -2.256, what is the decision regarding the hypothesis that the training was effective in improving customer relationships when tested at a 0.01 significance level?

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 60 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 12 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

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 $1000, 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?

If the decision is to reject the null hypothesis at the 5% level of significance, what are the acceptable alternate hypothesis and rejection region?

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 p_a - p_b = 0. ii. The alternate hypothesis is p_a - p_b > 0. iii. The z-statistic is 3.40.

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 p_a - p_b = 0. ii. The alternate hypothesis is p_a - p_b $\neq$ 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?

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?

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences, they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow: Determine the calculated value oft. Was the training effective in improving customer relationships when tested at a 0.05 level of significance?

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 $1000, 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? If you use the 5% level of significance, what is the critical t value?

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. If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population. ii. If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances. iii. When sample sizes are less than 30, a test for the differences between two population means has n - 1 degrees of freedom.

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 $1000) 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 decision at the 5% level of significance?

Of 150 adults who tried a new peach-flavoured peppermint patty, 81 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.