Exam 10: Statistical Inferences About Two Populations

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 ___.

The F test of two population variances is extremely robust to the violations of the assumption that the populations are normally distributed.

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 appropriate decision is ___.

A random sample of 400 items from a population shows that 160 of the sample items possess a given characteristic.A random sample of 400 items from a second population resulted in 110 of the sample items possessing the characteristic.Using this data,a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic.The resulting confidence interval 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 If $\alpha$ = 0.05,the appropriate decision 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.If $\alpha$ = 0.05,the observed F value is ___.

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 point estimate for the difference in the means of these two populations is ___.

The difference in two sample means is normally distributed for sample sizes ≥ 30,only if the populations are normally distributed.

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 alternate hypothesis is ___.

Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

If the sample sizes are greater than 30 and the population variances are known,the basis for statistical inferences about the difference in two population means using two independent random samples is the z statistic,regardless of the shapes of the population distributions.

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

If a 90% confidence interval for the difference in the two population means contains zero,then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 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 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 ___.

Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

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 ___.

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 ___.

A researcher is interested in estimating the difference in two population proportions.A sample of 400 from each population results in sample proportions of .61 and .64.A 90% confidence interval for the difference in the population proportions 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 observed z value 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.A 95% confidence interval would be ___.