Exam 10: Statistical Inferences About Two 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, the observed F value is _______.

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

A university administrator believes that business students are more likely to be working and going to school than their liberal arts majors.This information may lead to the business school offering courses in the evening hours while the liberal arts college maintains a daytime schedule.To test this theory, the proportion of business students who are working at least 20 hours per week is compared to the proportion of liberal arts students who are working at least 20 hours per week.A random sample of 600 from the business school has been taken and it is determined that 480 students work at least 20 hours per week.A random sample of 700 liberal arts students showed that 350 work at least 20 hours per week.The observed z for this is _______.

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

You are interested in determining the difference in two population means.You select a random sample of 8 items from the first population and 8 from the second population and then compute a 95% confidence interval.The sample from the first population has an average of 12.2 and a standard deviation of 0.8.The sample from the second population has an average of 11.7 and a standard deviation of 1.0.Assume that the values are normally distributed in each population and that the population variances are approximately equal.The corresponding critical t value from the table 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 can assume that the differences are normally distributed in the population.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 critical 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 _______.

A researcher wants to estimate the difference in the means of two populations.A random sample of 36 items from the first population results in a sample mean of 430.A random sample of 49 items from the second population results in a sample mean of 460.The population standard deviations are 120 for the first population and 140 for the second population.From this information, a 95% confidence interval for the difference in population means 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 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 372 orders within 24 hours.Maureen's alternative hypothesis is _______.

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 = 15 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 2 and $\sigma$ ₂ = 3.With $\alpha$ = .01, the critical z value is _________________.

The F statistic is a ratio of two independent sample variances.

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 observed z value is ___________________.

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: Pair Group 1 Group 2 1 10 12 2 8 9 3 11 11 4 8 10 5 9 12 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 _______.

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.Assuming $\alpha$ = 0.01, the appropriate decision is ______.

A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs.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 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40.He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90.He is using an alpha value of .10 to conduct this test.Assuming that the populations are normally distributed and that the population variances are approximately equal, the degrees of freedom for this problem are _______.

A researcher is conducting a matched-pairs study.She gathers data on each pair in the study resulting in: Pair Group 1 Group 2 1 10 12 2 8 9 3 11 11 4 8 10 5 9 12 Assume that the data are normally distributed in the population.The degrees of freedom in this problem are _______.

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: Pair Group 1 Group 2 1 10 12 2 8 9 3 11 11 4 8 10 5 9 12 Assume that the data are normally distributed in the population.To obtain a 95% confidence interval, the table t value would be _______.

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 wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings.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 taking the medication.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 _______.