Exam 10: Statistical Inferences About Two Populations

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 _______.

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 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 -1)degrees of freedom.

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 critical t value used from the table for this 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 = 0.15 with n₁ = 8,and,for Stockton,the results were s₂² = 0.04 with n₂ = 10. Assume that rod lengths are normally distributed in the population If $\alpha$ = 0.05,the observed F value 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 having 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 critical 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 _______.

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 = 0.15 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 _________.

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 ___________________.

You are interested in determining whether the mean price of electricity offered by solar companies is different in the southern states than in the northern states.You select a random sample of 8 solar companies from the southern states and 11 from the northern states.For the southern states,the average price is 12.2 cents per kWh (kilowatt hour)and the standard deviation is 0.8 cents per kWh.For the northern states,the average and standard deviation are 11.7 and 1.0 cents per kWh respectively.If you use a significance level α = 0.10 and assuming the values are normally distributed in both populations,the critical t 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 observed F value 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.The point estimate for the difference in means of these two populations 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 plans to test this hypothesis using a random sample of 81 individuals from each suburb.His 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 who have completed 75% or more of the recommended training for 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 deviations 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 ______.

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 alternative 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. Assuming that the values are normally distributed in each population,the researcher would like to use the t procedure with pooled standard deviation using the F test.Using $\alpha$ = 0.05,the observed F value is _______.

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 _______.

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 appropriate decision is ___________________.