Exam 10: Statistical Inferences About Two Populations

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)degrees of freedom.

A researcher is interested in testing to determine if the mean of population one is greater than the mean of population two.The null hypothesis is that there is no difference in the population means (i.e. ,the difference is zero).The alternative hypothesis is that there is a difference (i.e. ,the difference is not equal to zero).He randomly selects a sample of 9 items from population one resulting in a mean of 14.3 and a standard deviation of 3.4.He randomly selects a sample of 14 items from population two resulting in a mean of 11.8 and a standard deviation 2.9.He is using an alpha value of .10 to conduct this test.Assuming that the populations are normally distributed,the degrees of freedom for this problem are ___.

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 null hypothesis is ___.

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 95% confidence interval,the table t value would be ___.

If the populations are normally distributed but the population variances are unknown,the t statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

A researcher wishes to determine the difference in two population means.To do this,she randomly samples 9 items from each population and computes a 90% confidence interval.The sample from the first population produces a mean of 780 with a standard deviation of 240.The sample from the second population produces a mean of 890 with a standard deviation of 280.Assume that the values are normally distributed in each population.The t value used for this is ___.

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.Claude's alternate hypothesis is ___.

Lucy Baker is analyzing demographic characteristics of two television programs,Lost (population 1)and Heroes (population 2).Previous studies indicate no difference in the ages of the two audiences.(The mean age of each audience is the same. )Lucy plans to test this hypothesis using a random sample of 100 from each audience.Her null hypothesis 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.Assuming $\alpha$ = 0.05,the critical z value 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 6.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05,the observed F value is ___.