Exam 10: Statistical Inferences About Two Populations

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 its 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 ___.

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.

In a set of matched samples, each data value in one sample is related to or matched with a corresponding data value in the other sample.

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.

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 ___.

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 ___.

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 ___.

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.

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 ___.

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.

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 ___.

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.)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 wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores.The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero.Scores are obtained on the subjects both before and after the treatment.After subtracting the after scores from the before scores, the average difference is computed to be -2.40 with a sample standard deviation of 1.21.Assume that the differences are normally distributed in the population.The observed t value for this test 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.The point estimate of 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 appropriate decision 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 ___.

Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant.He wants to prove that Raymondville residents (population 1)dine out more often than Rosenberg residents (population 2).Denny commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 families 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 appropriate decision 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 a two-tailed test is performed, the null hypothesis would be rejected if the observed value of t 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 alternate hypothesis is ___.

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