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

A broth used to manufacture a pharmaceutical product has its sugar content, in milligram: milliliter, measured several times on two successive days. The results are shown below. Can you conclude that the variability of the process is greater on the second day than on tl day? Use the $\alpha = 0.01$ level of significance. per first

In comparing the two standard deviations below, what test value and degrees of freedom should be used in an $F$ test? Sample 1 Sample 2 Standard deviation 7 3 Sample size 14 23

A poll found that 37% of male voters and 45% 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

A study of cats and dogs found that 30 of 60 cats and 11 of 40 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?

When subjects are matched according to one variable, the matching process does not eliminate the influence of other variables.

The critical value for a two-tailed $F$ test is $2.65$ when $\alpha = 0.05$ , the sample size from which the variance for the numerator was obtained is 10 , and the sample size from which the variance for the denominator was obtained is 15 .

If the test value for the difference between the means of two large samples is $1.43$ when the critical value is $1.96$ , the null hypothesis should not be rejected.

$\text { In the } F \text { distribution the mean value of } F \text { is approximately equal to }$ _______

An automobile manufacturer wishes to test that claim that synthetic motor oil can improv mileage (in miles per gallon, or mpg). The table below shows the gas mileages, in mpg, o that used synthetic motor oil. The table also shows the gas mileages in mpg of six cars tha using conventional motor oil (the controls). Synthetic: 24 28 27 28 26 26 Control: 26 25 25 27 27 27 Can you conclude that the mean gas mileage for cars using synthetic motor oil is more the the mean for the controls? Use the $\alpha = 0.05$ level of significance. as

Find $\bar { p }$ and $\bar { q }$ , if $X _ { 1 } = 11 , n _ { 1 } = 30 , X _ { 2 } = 28$ , and $n _ { 2 } = 80$ .

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 $X _ { 1 }$ and $X _ { 2 }$ as given in the table. Consequently, $D = X _ { 1 } - X _ { 2 }$ . Determine the mean of the differences.

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 $X _ { 1 }$ and $X _ { 2 }$ as given in the table. Consequently, $D = X _ { 1 } - X _ { 2 }$ . What critical value should be used at $\alpha = 0.05 ?$

The average credit card debt for a recent year was $\$ 8824$ . Five years earlier the average credit card debt was $\$ 8159$ . Assume sample sizes of 35 were used and the population standard deviations of both samples were $\$ 1396$ . Is there evidence to conclude that the average credit card debt has increased? Use $\alpha = 0.05$ . a. State the hypotheses. b. Find the critical value. c. Compute the test statistic. d. Make the decision. e. Summarize the results.

An $F$ -test with 13 degrees of freedom in the numerator and 9 degrees of freedom in the denominator produced a test statistic whose value was $3.36$ . The null and alternate hypotheses were $H _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 }$ versus $H _ { 1 } : \sigma _ { 1 } < \sigma _ { 2 }$ . Do you reject $H _ { 0 }$ at the $\alpha = 0.05$ level?

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 $X _ { 1 }$ and $X _ { 2 }$ as given in the table. Consequently, $D = X _ { 1 } - X _ { 2 }$ . Compute the standard deviation of the differences.

The concentration of hexane (a common solvent) was measured in units of micrograms per liter for a simple random sample of nineteen specimens of untreated ground water taken near a municipal landfill. The sample mean was $508.4$ with a sample standard deviation of 4.3. Sixteen specimens of treated ground water had an average hexane concentration of $506.1$ with a standard deviation of 4.7. It is reasonable to assume that both samples come from populations that are approximatel normal. Can you conclude that the mean hexane concentration is less in treated water thar untreated water? Use the $\alpha = 0.01$ level of significance.

Following is a sample of five matched pairs. Sample 1 20 20 23 18 22 Sample 2 23 16 15 14 18 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 $H _ { 1 } : \mu _ { \mathrm { d } } > 0$ . Can you reject $H _ { 0 }$ at the $\alpha = 0.01$ level of significance?

A test was made of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ versus $H _ { 1 } : \mu _ { 1 } < \mu _ { 2 }$ . The sample means were $\bar { x } _ { 1 } = 13$ and $\bar { x } _ { 2 } = 12$ , the sample standard deviations were $s _ { 1 } = 4$ and $s _ { 2 } = 3$ , and the sample sizes were $n _ { 1 } = 16$ and $n _ { 2 } = 15$ . How many degrees of freedom are there for the test statistic?