Exam 10: Statistical Inferences About Two Populations

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.

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.

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 = 15 times per month and ₂ = 14 times per month.Assume that $\sigma$ ₁ = 2 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the appropriate decision is ___.

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?

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.

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.Assuming a two-tail test and $\alpha$ = .05, the observed z 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 observed z 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 plans to test this hypothesis using a random sample of 81 families from each suburb.His null hypothesis 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, Tamara's alternate hypothesis 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 t value used for this is ___.

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

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 ___.

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 356 orders within 24 hours.Assuming $\alpha$ = 0.05, the observed 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 8.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05, 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 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 ___.

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

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.

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 observed 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 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 = 0.15 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 ___.

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 ___.