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

Determine the value of $\alpha$ as shown below in the graph of an $F$ distribution. The degrees $c \quad 86)$ _______freedom for the numerator are seven, and the degrees of freedom for the denominator are

A marketing firm asked a random set of married and single men how much they were willing to spend on a vacation. Is there sufficient evidence at $\alpha = 0.05$ to conclude that is there a difference in the two amounts? Married Men Single Men Sample size 70 70 Sample mean \ 880 \ 825 Population variance 5700 7900

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 critical value at $\alpha = 0.05 ?$

Following is a sample of five matched pairs. Sample 1 23 26 18 32 28 Sample 2 19 14 16 12 14 Let $\mu _ { 1 }$ and $\mu _ { 2 }$ represent the population means and let $\mu _ { \mathrm { d } } = \mu _ { 1 } - \mu _ { 2 }$ . A test will be made of the hypotheses $H _ { 0 } : \mu _ { \mathrm { d } } = 0$ versus $H _ { 1 } : \mu _ { \mathrm { d } } > 0$ . Compute the test statistic.

The following MINITAB output display presents the results of a hypothesis test for the difference $\mu _ { 1 } - \mu _ { 2 }$ between two population means. Difference $= \operatorname { mu } ( \mathrm { X } 1 ) - \operatorname { mu } ( \mathrm { X } 2 )$ Estimate for difference: $- 26.338$ $95 \%$ CI for difference: $( - 47.152 , - 5.524 )$ $\mathrm { T }$ -Test of difference $= 0 ($ vs not $= ) :$ T-Value $= - 2.480133$ $\mathrm { P } -$ Value $= 1.979112 \quad \mathrm { DF } = 23$ How many degrees of freedom are there for the test statistic?

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?

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 A 12 Mean StDev SE Mean B 8 46.021 22.014 6.355 B 40.649 27.337 9.665 Difference $= m u ( X 1 ) - m u ( X 2 )$ Estimate for difference: $25.372$ $95 \%$ CI for difference: $( 2.700,48.044 )$ T-Test of difference $= 0 ($ vs not $= ) : \quad$ T-Value $= 2.193456$ $\mathrm { P } - \mathrm { Value } = 0.04706 \mathrm { DF } = 13$ What is the alternate hypothesis?

When the subjects are paired or matched in some way, samples are considered to be .

In a random sample of 200 men, 125 said they used seat belts. In a random sample of 300 women, 65 said they used seat belts. Test the claim that women are less safety-conscious than men at $\alpha = 0.01$ . Use the $P$ -value method.

Two groups were polled about their attitudes towards capital punishment. In one group 30 out of 100 favored capital punishment, and in the other group 40 out of 80 favored Capital punishment. Calculate an appropriate test value test the hypothesis that the Population proportions are the same.

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

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 appropriate test value for a $t$ test?

A poll found that 39% of male voters and 42% of female voters support a particular candidate. To test whether this candidate has equal levels of support between male and Female voters, the alternative hypothesis should be

In an experiment to determine whether there is a systematic difference between the weigh obtained with two different mass balances, six specimens were weighed, in grams, on eac balance. The following data were obtained: Specimen 1 14.86 14.83 2 9.44 9.41 3 11.99 11.99 4 9.27 9.26 5 6.13 6.13 6 13.78 13.76 Compute the test statistic.

A pharmaceutical company is testing the effectiveness of a new drug for lowering cholest part of this trial, they wish to determine whether there is a difference between the effectiv for women and men. At $\alpha = 0.05$ , what is an appropriate test value? Women Men Sample size 50 40 Mean effectiveness 7.9 8 Population variance 3.1 3.6 ol. As

The football coach at State University wishes to determine if there is a change in offensiv 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. State the null and alternative hypotheses.

A garden seed wholesaler wishes to test the claim that tomato seeds germinate faster whes individual seed is "pelletized" within a coating of corn starch. The table below shows the germination times, in days, of six pelletized seeds. The table also shows the germination 1 days of six un-coated seeds (the controls). Pelletized: 9 9 10 8 6 6 Control: 9 11 12 9 12 11 Can you conclude that the mean germination time for pelletized seeds is less than the mea for the un-pelletized seeds? Use the $\alpha = 0.05$ level of significance.

When comparing the means of samples from two normally distributed populations, if the samples are independent and the population variances are known, the $z$ test can be used.

A recent survey reported that in a sample of 300 students who attend two-year colleges, 105 work at least 20 hours per week. Additionally, in a sample of 225 students attending Private four-year universities, only 20 students work at least 20 hours per week. What is The test value for a test of the difference between these two population proportions?