Exam 10: Two-Sample Tests of Hypothesis

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?

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. What is the value of the calculated test statistic?

Of 250 adults who tried a new multi-grain cereal, Wow!, 187 rated it excellent; of 100 children sampled, 66 rated it excellent. What test statistic should we use?

The results of a mathematics placement exam at Mercy College for two campuses is as follows: We want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2. Using the printout above, what decision(s) can be made?

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 55 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? If we let East Vancouver be population 1 and Oshawa be population 2, what is the null 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 64 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 20 single-earner and 12 dual-earner couples studied. State the decision rule, the value of the test statistic, and your decision.

i. If samples taken from two populations are not independent, then a test of paired differences is applied. ii. The paired difference test has (n - 1) degrees of freedom. iii. The paired t test is especially appropriate when the sample sizes of two groups are the same.

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 $\pm$ 2.58. ii. The z-statistic is 3.40. iii. Your decision is to reject the null hypothesis.

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 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 p_a - p_b > 0. ii. The alternate hypothesis is p_a - p_b $\neq$ 0. iii. The pooled estimate of the population proportion is 0.36.

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:

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): What is the decision at the 5% 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? This example is what type of test?

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. The critical value of t for a two-tail test of the difference of two means, a level of significance of 0.10 and sample sizes of seven and fifteen, is $\pm$ 1.734.

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. When sample sizes are less than 30, a test for the differences between two population means has n- 1 degrees of freedom.

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 computed value of t?

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: What are the null and alternative 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 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 $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 degree of freedom?