Exam 10: Two-Sample Tests of 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: For a 0.01 significance level, what is the critical value?

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?

Using two independent samples, two population means are compared to determine if a difference exists. The number in the first sample is fifteen and the number in the second sample is twelve. How many degrees of freedom are associated with the critical 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 $\neq$ 0. ii. Using the 1% level of significance, the critical value is $\pm$ 2.58. iii. The z-statistic is 3.40.

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?

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 hypothesisp₁not equal top₂, what is the null 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: What is the decision at the 5% level of significance?

The net weights of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are (in grams): Testing the claim at the 0.05 level the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, what is the critical value?

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. 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.

Administering the same test to a group of 15 students and a second group of 15 students to see which group scores higher is an example of:

i. 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. ii. We use the pooled estimate of the proportion in testing the difference between two population proportions. iii. The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

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 decision at the 5% 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. Assume calculated t to be +2.70; what is the decision at the 0.01 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?

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?

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.

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?

Suppose we are testing the difference between two proportions at the 0.05 level of significance. If the computed z is -1.07, what is our decision?

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.

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