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 null hypothesis?

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. If the p-value obtained from the computer printout is 0.025, does this give sufficient evidence to conclude that the mean level of job satisfaction for women with working husbands is more than that of those whose husbands don't work?

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 p_a - p_b $\neq$ 0. ii. The proportion of sales made in Market Area 1 is 0.40. iii. The proportion of sales made in Market Area 2 is 0.33.

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.

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.

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

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 p_a - p_b > 0. ii. The z-statistic is 3.40. iii. Your decision is to accept the null hypothesis.

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: The calculated value oft. is -2.542. 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? What is the alternate hypothesis?

Suppose we test H0: $\pi$ 1 = $\pi$ 2 at the 0.05 level of significance. If the z-test statistic is -1.07, what is our 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. What is the decision at the 1% 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? What is the value of calculated t?

i. If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed. ii. 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. iii. The critical value for the claim that the difference of two means is less than zero with a level of significance of 0.025 and sample sizes of nine and seven, is -2.179.

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. 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.

For a hypothesis comparing two population means, H₀: $\mu$ ₁ $\le$ $\mu$ ₂, what is the critical value for a one-tailed hypothesis test, using a 5% significance level, with both sample sizes equal to 13? Assume the population standard deviations are equal.

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?

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. Ball Bearings Hypothesis Test: Independent Groups (t-test, pooled variance) What is the decision at the 1% level of significance?

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. If the p-value obtained from the computer printout is 0.055, does this give sufficient evidence to conclude that the mean level of job satisfaction for women with working husbands is more than that of those whose husbands don't work?

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?

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