Exam 10: Statistical Inferences About Two Populations

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 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 critical F 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 a two-tailed test is performed, the null hypothesis would be rejected if the observed value of t 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 the 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 ______.

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 _______.

When testing for the difference between two population proportions we use a pooled estimate of the proportion.

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

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 the 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 observed z 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 ______.

If the variances of the two populations are not 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.

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: $\bar { x }$ ₁ = 43 years and $\bar { x }$ 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 _________________.

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 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 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 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.Assuming $\alpha$ = 0.05, the appropriate decision 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 observed z value is ______.

Suppose that the proportion of young adults who read at least one book per month is 0.15, and this proportion is the same in Boston and New York.Suppose that samples of 400 are randomly drawn from each city.The standard deviation of the differences for the sampling distribution between the first sample proportion and the second sample proportion (used to calculate the z score)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 _______.

When finding a confidence interval for the difference between two population proportions we use a pooled estimate of the proportion.

An appropriate sampling plan to determine if there is a difference in the speed of a wireless router from two different manufacturers, consists of a network manager drawing independent samples of wireless routers from the two manufacturers and comparing the difference in the sample means for the connection speed.

If the populations are normally distributed and the variances of the two populations are not equal, it is appropriate to use the "unpooled" formula to determine the t-statistic for the hypothesis test of the difference in the two population means.