Exam 10: Statistical Inferences About Two Populations

To determine if there is a difference in the speed of a wireless router from two different manufacturers a network manager will draw independent samples of wireless routers from the two manufacturers and compare the difference in the sample means for the connection speed.

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

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 _______.

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 observed t value for this test 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 appropriate decision is _______.

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 $\sigma$ ₁ = 0.2 and $\sigma$ ₂ = 0.3.With $\alpha$ = .05,the critical z value 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 __________.

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 = 0.10 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 ________.

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. A 90% confidence interval for the difference in the population proportions 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 and that the population variances are approximately equal.The critical t value used from the table for this 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 sample standard deviation (s_d)of the differences 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.) 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 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 _______.

If the populations are normally distributed and the variances of the two populations are 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.

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 ___________________.

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.) 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 appropriate decision is _________________.

The ratio of two independent sample variances follows the F distribution.

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 _______.

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 ____.

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: 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 _________________.