Exam 9: Testing the Difference Between Two Means, Two Variances, and Two Proportions

A running coach wanted to see whether runners ran faster after eating spaghetti the night before. A group of six runners was randomly chosen for this study. Each ran a 5 kilometer race after having a normal dinner the night before, and then a week later, reran the same race after having a spaghetti dinner the night before. The times for their races are shown in the table below. What test value should be used in a t test for these dependent samples?

Use Table H from the textbook to find the critical value for a right-tailed F test with α = 0.05, d.f.N. = 21, and d.f.D. = 20.

Which of the following represent dependent samples. i. Life spans of pairs of siblings. ii. Life spans of randomly-selected pairs of people iii. Life spans of pairs of mothers and daughters

A marketing firm asked a random set of married women and married men how much they were willing to spend for jewelry as a present for their spouse. Can the firm conclude, at = 0.05, that the two groups have a different willingness to spend?

A reporter bought hamburgers at randomly selected stores of two different restaurant chains, and had the number of Calories in each hamburger measured. Can the reporter conclude, at = 0.05, that the hamburgers from the two chains have a different number of Calories?

A study of cats and dogs found that 39 of 60 cats and 21 of 50 dogs slept more than 10 hours per day. At the 0.05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportions of cats and dogs that sleep more than 10 hours per day?

Find the proportion given n = 32 and X = 8.

Given the variances of the two samples below, find the test value and the degrees of freedom that should be used in an F test.

68% of students at a university live on campus. A random sample found that 24 of 40 male students and 43 of 55 of female students live on campus. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of male and female students who live on campus?

The formula used in the z test for comparing the means from two independent populations is _______________.

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount spent on lunches. The variance of the cost of nine business dinners (in US$) was 6.12 and the variance on 12 lunches was 0.87. What test value should be used in an F test?

Use the following to answer questions Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtained the data shown in the table below. -What is the critical value at α = 0.05?

An educational researcher is analyzing the test scores for physics students taught using two different methods - a traditional method, and a web-based self-paced method. Can he conclude, at = .05, that the test scores in the web-based self-paced method are lower?

For the samples summarized below, test the hypothesis that the two variances are equal, at α = 0.05

A local charity believes they receive more money from people in the River Heights neighborhood than from people in the Lakeview neighborhood. They conducted a survey of 24 people randomly selected form each neighborhood and recorded the results. At α = 0.01, is their hypothesis correct?

One uses a t test when comparing two variances or standard deviations.

Use the following to answer questions Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtained the data shown in the table below. -What is the appropriate test value for a t test?

A poll found that 47% of male voters and 50% of female voters support a particular candidate. To test whether this candidate has equal levels of support between male and female voters, the null hypothesis should be

In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test?

Use the following to answer questions A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X₁ and X₂ as given in the table. Consequently, D = X₁-X₂. -Compute the standard deviation of the differences.