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

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 obtair data shown in the table below. Imported Wine Domestic Wine =\ 7.03 =\ 9.78 =\ 2.31 =\ 3.62 n=15 n=16 What is the null hypothesis?

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 $\alpha = .05$ , that the test scores in the web-based self-paced method are lower? Traditional Web-based Self-paced Sample size 60 80 Mean test score 86 83 Population variance 24 34

The critical value for a right-tailed $F$ test is $2.57$ when $\alpha = 0.025$ , the degrees of freedom for the numerator are 15 , and the degrees of freedom for the denominator are 20 .

A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states. At $\alpha = 0.05$ , is there enough evidence to conclude that there is a difference in the interest rates paid by the two states? State A State B Sample size 60 40 Mean interest rate (\%) 3.5 3.9 Population variance 0.02 0.04

A test was made of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ versus $H _ { 1 } : \mu _ { 1 } < \mu _ { 2 }$ . The sample means were $\bar { x } _ { 1 } = 11$ and $\bar { x } _ { 2 } = 9$ , the sample standard deviations were $s _ { 1 } = 7$ and $s _ { 2 } = 5$ , and the sample sizes were $n _ { 1 } = 15$ and $n _ { 2 } = 13$ . Is $H _ { 0 }$ rejected at the $0.05$ level? (Hint: First compute the value of the test statistic.)

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 car salesman claims that the variance of prices on convertibles is higher than the variance of prices on station wagons. The standard deviation of the list price on 16 Convertibles is $6800 and the standard deviation on 24 station wagons is $3900. What Should the test value be?

A sociologist wants to determine if the life expectancy of people in Africa is less than the expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia =63.3. =65.2. =9.1. =7.3. =120 =150 What is an appropriate null hypothesis?

The football coach at State University wishes to determine if there is a decrease in offensi production between the first half and the second half of his team's recent games. The tabli shows the first-half and second-half offensive production (measured in total yards gained for the past six games. Compute the test statistic.

Joan has just moved into a new apartment and wants to purchase a new couch. To determine if there is a difference between the average prices of couches at two different stores, she collects the following data. Test the hypothesis that there is no difference in the average price. Use $\alpha = 0.05$ . Store 1 Store 2 =\ 650 =\ 680 =\ 43 =\ 52 =42 =45

A sociologist wants to determine if the life expectancy of people in Africa is less than the expectancy of people in Asia. The data obtained is shown in the table below. Africa Asia =63.3. =65.2. =9.1. =7.3. =120 =150 Calculate the critical value. Use $\alpha = 0.05$ .

The following MINITAB output display presents the results of a hypothesis test for the difference $\mu _ { 1 } - \mu _ { 2 }$ between two population means. Two-sample T for X1 vs X2 N Mean StDev SE Mean A 12 66.021 22.014 6.355 B 8 40.649 27.337 9.665 Difference $= \operatorname { mu } ( \mathrm { X } 1 ) - \mathrm { mu } ( \mathrm { X } 2 )$ Estimate for difference: $25.372$ $95 \%$ CI for difference: $( 2.700,48.044 )$ $\mathrm { T }$ -Test of difference $= 0 ($ vs not $= ) : \quad \mathrm { T } - \mathrm { Value } = 2.193456$ P-Value $= 0.04706 \mathrm { DF } = 13$ Can you reject $H _ { 0 }$ rejected at the $\alpha = 0.10$ level?

Twelve dieters lost an average of 5.2 pounds in 6 weeks when given a special diet plus a "fat-blocking" herbal formula. A control group of twelve other dieters were given the Same diet, but without the herbal formula, and lost an average of 4.5 pounds during the Same time. The standard deviation of the "fat-blocker" sample was 2.8 and the standard Deviation of the control group was 2.5. Find the 95% confidence interval for the Differences of the means.

A researcher hypothesized that the variation in the car rental rates (in US\$/day) at a major city airport is less than in the car rental rates down town. A survey found that the variance of the rental rates on 8 cars at the airport was $35.7$ while the variance of the rental rates on 5 cars down town was $50.4$ . What test value should be used in a $F$ test?

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 $\alpha = 0.05$ , that the two groups have a different willingness to spend? Women Men Sample size 9 16 Sample mean \ 160 \ 205 Sample standard deviation \ 34 \ 38

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? Freshmen Seniors Sample size 80 70 Sample mean \ 460 \ 440 Population std. dev. \ 52 \ 63

To determine whether two sample variances are equal, a researcher can use a(n) .

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for the difference between two means. The sample sizes are $n _ { 1 } = 7$ and $n _ { 2 } = 12$ . How many degrees of freedom did the calculator use?

Consider the null hypothesis $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ . If the confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ does not contain 0 , the null hypothesis should be rejected.