Exam 10: Statistical Inferences About Two Populations

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 critical t value from the table is ___.

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

If a 98% confidence interval for the difference in the two population means does not contain zero,then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.02 level of significance.

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 degrees of freedom in this problem are ___.

If the variances of the two populations are not equal,it is appropriate to use the "pooled" formula to determine the t statistic for the hypothesis test of the difference in the two population means.

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.

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.What is the probability that the differences in sample proportions will be greater than 0.02?

Test hypotheses about the difference in two population variances using the F distribution.

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 alternate hypothesis 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.

Sets of matched samples are also referred to as independent samples.

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 critical F value 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 null hypothesis is ___.

To determine if there is a difference in the strength of steel produced from two different production processes,a process manager will draw independent samples from the two processes and compare the difference in the sample means.

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,Tamara's alternate hypothesis 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 = 0.15 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 appropriate decision is ___.

Test hypotheses and develop confidence intervals about the difference in two dependent populations.

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,Tamara's null hypothesis is ___.

Sets of matched samples are also referred to as dependent samples.

If the variances of the two populations are equal,it is appropriate to use the "pooled" formula to determine the t statistic for the hypothesis test of the difference in the two population means.