Exam 10: Statistical Inferences About Two Populations

A researcher is conducting a matched?pairs study.She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population.The level of significance is selected to be 0.10.If a two-tailed test is performed,the null hypothesis would be rejected if the observed value of t is _______.

Tamara Hill,fund manager of the Hill Value Fund,manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio,i.e.,one with a price variance less than that of the S&P 500 index.Moreover,she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1)was 25,and for the last seven quarters the price variance for XYC common (population 2)was 8.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05,the appropriate decision is _______.

If the sample sizes are small,but the populations are normally distributed and the population variances are known,the z-statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests,Claude Carter,Quality Assurance Manager,has recommended purchasing rods from Redding Rods,Inc.(population 1),rather than Stockton Steel (population 2),since Redding's rods had less variability in length.Recently,Stockton revised it rod shearing operation,and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes.The results for Redding were s₁² = 0.10 with n1 = 8,and,for Stockton,the results were s₂² = 0.05 with n2 = 10.Assume that rod lengths are normally distributed in the population.If $\alpha$ = 0.05,the critical F value is _____________.

Maureen McIlvoy,owner and CEO of a mail order business for wind surfing equipment and supplies,is reviewing the order filling operations at her warehouses.Her goal is 100% of orders shipped within 24 hours.In previous years,neither warehouse has achieved the goal,but the East Coast Warehouse has consistently out-performed the West Coast Warehouse.Her staff randomly selected 200 orders from the West Coast Warehouse (population 1)and 400 orders from the East Coast Warehouse (population 2),and reports that 190 of the West Coast Orders were shipped within 24 hours,and the East Coast Warehouse shipped 372 orders within 24 hours.Maureen's alternative hypothesis is _______.

Golf course designer Roberto Langabeer is evaluating two sites,Palmetto Dunes and Ocean Greens,for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 individuals from each suburb,and reported the following: 1 = 16 times per month and 2 = 14 times per month.Assume that $\sigma$ 1 = 4 and $\sigma$ 2 = 3.With $\alpha$ = .01,the observed z value is _________________.

A researcher is conducting a matched?pairs study.She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population.The level of significance is selected to be 0.10.If the alternative hypothesis is that the average difference is greater than zero,the null hypothesis would be rejected if the observed value of t is _______.

To test hypotheses about the equality of two population variances,the ratio of the variances of the samples from the two populations is tested using the F test.

A researcher believes a new diet should improve weight gain.To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected.The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds,while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds.Assume that the values are normally distributed in each population and that the population variances are approximately equal.Using $\alpha$ = 0.05,the observed t value for this test is _______.

Tamara Hill,fund manager of the Hill Value Fund,manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio,i.e.,one with a price variance less than that of the S&P 500 index.Moreover,she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1)was 25,and for the last seven quarters the price variance for XYC common (population 2)was 8.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05,the observed F value is _______.

Lucy Baker is analyzing demographic characteristics of two television programs,American Idol (population 1)and 60 Minutes (population 2).Previous studies indicate no difference in the ages of the two audiences.(The mean age of each audience is the same.)Her staff randomly selected 100 people from each audience,and reported the following: 1 = 43 years and 2 = 45 years.Assume that $\sigma$ 1 = 5 and $\sigma$ 2 = 8.With a two-tail test and $\alpha$ = .05,the critical z values are _________________.

A researcher believes a new diet should improve weight gain.To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected.The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds,while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds.Assuming that the values are normally distributed in each population,the researcher would like to use the t procedure with pooled standard deviation using the F test.Using $\alpha$ = 0.05,the observed F value is _______.

In order to construct an interval estimate for the difference in the means of two normally distributed populations with unknown but equal variances,using two independent samples of size n₁ and n₂,we must use a t distribution with (n₁ + n₂ − 2)degrees of freedom.

Tamara Hill,fund manager of the Hill Value Fund,manages a portfolio of 250 common stocks.Tamara is searching for a 'low risk' issue to add to the portfolio,i.e.,one with a price variance less than that of the S&P 500 index.Moreover,she assumes an issue is not 'low risk' until demonstrated otherwise.Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1)was 25,and for the last seven quarters the price variance for XYC common (population 2)was 6.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05,the observed F value is _______.

A researcher is conducting a matched?pairs study.She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population.The sample standard deviation (s_d)of the differences is _______.

The F statistic is a ratio of two independent sample variances.

To determine if there is a difference in the speed of a wireless router from two different manufacturers a network manager will draw independent samples of wireless routers from the two manufacturers and compare the difference in the sample means for the connection speed.

A researcher is estimating the average difference between two population means based on matched?pairs samples.She gathers data on each pair in the study resulting in: Assume that the data are normally distributed in the population.To obtain a 90% confidence interval,the table t value would be _______.

Lucy Baker is analyzing demographic characteristics of two television programs,American Idol (population 1)and 60 Minutes (population 2).Previous studies indicate no difference in the ages of the two audiences.(The mean age of each audience is the same.)Her staff randomly selected 100 people from each audience,and reported the following: 1 = 43 years and 2 = 45 years.Assume that $\sigma$ 1 = 5 and $\sigma$ 2 = 8.Assuming a two-tail test and $\alpha$ = .05,the observed z value is _________________.

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.The standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion (used to calculate the z score)is _______.