Exam 10: Statistical Inferences About Two Populations

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?

You are evaluating investing in a cognitive training company.For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem-solving skills.You select a random sample of new users and get test scores for each participant in the sample.The test score is a composite of reading comprehension and problem-solving skills.Two months later, you randomly select 15 users from the original sample who have completed 75% or more of the recommended training in the last two months and have them take a test similar to the initial test.You are interested in determining whether the average test score before training is different than the average test score after training for this sample.The after-training average is 92.8, which is 2.7 points higher than the before-training average.The sample standard deviation of the differences is 1.2.You can assume that the differences are normally distributed in the population.The degrees of freedom for this test are ______.

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto plans to test this hypothesis using a random sample of 81 individuals from each suburb.His null hypothesis is __________.

A researcher believes a new diet should improve weight gain.To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected.The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds.Assume that the values are normally distributed in each population and that the population variances are approximately equal.Using $\alpha$ = 0.05, the observed t value for this test is _______.

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.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 ________.

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.

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 these data, a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic.The resulting confidence interval 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.Maureen's null hypothesis is ____.

You are evaluating investing in a cognitive training company.For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem-solving skills.You select a random sample of new users and get test scores for each participant in the sample.The test score is a composite of reading comprehension and problem-solving skills.Two months later, you randomly select 15 users from the original sample who have completed 75% or more of the recommended training in the last two months and have them take a test similar to the initial test.You are interested in determining whether the average test score before training is different than the average test score after training for this sample.The after-training average is 92.8, which is 2.7 points higher than the before-training average.The sample standard deviation of the differences is 1.2.You use a significance level of 0.10, and you can assume that the differences are normally distributed in the population.The t-value from the table for this test is ______.

Testing the difference in two population proportions is useful whenever the researcher is interested in comparing the proportion of one population that has certain characteristic with the proportion of the second population that has the same characteristic.

Your company is evaluating two cloud-based secured data storage services."Pie in the Sky," the newer service, claims its uploading and downloading speeds are faster than the older service, "Cloudy but Steady Skies." You need to make a decision based on published access times for both services at different times and for varying file sizes.To make your decision, you purchase a statistical study, which indicates that average download time for Pie in the Sky is 0.77 sec.per MB and for Cloudy but Steady Skies is 0.84.Assume that n₁ = n₂ = 50, $\sigma$ ₁ = 0.2 and $\sigma$ ₂ = 0.3.With $\alpha$ = .05, the appropriate decision is ______.

In conducting a matched-pairs hypothesis test, the null and alternative hypotheses always represent one-tailed tests.

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.

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 West Coast Warehouse has consistently out-performed the East 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 appropriate decision is ___________________.

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

Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course.He wants to prove that Palmetto Dunes residents (population 1)play golf more often than Ocean Greens residents (population 2).Roberto commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 16 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 4 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the observed z value is _________________.

Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1)and 60 Minutes (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 ____________.

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.

Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company.His goal is to have at least 90% of technical employees with up-to-date certifications.The north-east division typically has maintained higher rates of up-to-date certifications than the southern division.He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division.Maxwell's 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 null hypothesis is _______.