Exam 11: Two-Sample Tests of Hypothesis

Suppose we test H₀: π₁ = π₂ at the 0.05 level of significance. If the z-test statistic is -1.07, what is our decision?

When can a paired t-test be used to test a hypothesis of no difference between population means?

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 decision regarding the hypothesis that the training was effective in improving customer relationships?

The results of a mathematics placement exam at two different campuses of Mercy College follow: Given that the two population standard deviations are known, what is the p-value?

A sample of 250 adults tried the new multigrain cereal "Wow!" A total of 187 rated it as excellent. In a sample of 100 children, 66 rated it as excellent. Using the 0.1 significance level, the researcher wishes to show that adults like the cereal better than children. Which of the following 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. The results follow. What is the value of the test statistic to test for differences in the times?

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the degrees of freedom are computed as (n₁)(n₂) - 1.

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. The results follow. Let α = 0.05. Is the mean time to access the new website design shorter, or is (time for the old design - time for the new design) greater than zero? Express your answer in terms of the null hypothesis.

In a market test of a new chocolate raspberry coffee, a poll of 400 people from Dobbs Ferry showed 250 preferred the new coffee. In Irvington, 170 out of 350 people preferred the new coffee. To test the hypothesis that there is no difference in preferences between the two villages, what is the null hypothesis?

To compare the effect of weather on sales of soft drinks, a distributor surveyed people in two regions of the country and asked if they purchased soft drinks in the last month. The following are the results. The distributor would like to know if there is a difference in sales between the two regions. What is the proportion of sales made in Region B?

A statistics professor wants to compare grades in two different classes of the same course. This is an example of _________ populations.

The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

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

A study by a bank compared the mean savings of customers who were depositors for three years or less with those who had been depositors for more than three years. The results of a sample are as follows. Assuming that the financial officer wants to show that there is a difference in the average savings balance between the two classes of depositors, the null hypothesis is ____________.

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.

If we are testing the difference between two population proportions, it is assumed that the two populations are approximately normal and have equal variances.

A committee that is 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 test if the reactions to the survey for office and plant personnel were the same, 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 favor of the proposal. What is the pooled estimate of the population proportion?

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 null hypothesis?

A sample of 250 adults tried the new multigrain cereal "Wow!" A total of 187 rated it as excellent. In a sample of 100 children, 66 rated it as excellent. Using the 0.1 significance level, the researcher wishes to show that adults like the cereal better than children. What test statistic should we use to compare the ratings of adults and children?

A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. At the .01 significance level, do women save more money than men? What is the value of the test statistic for this hypothesis test?