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 6.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05,the appropriate decision 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.A 0.05 level of significance is selected.Assume that the differences are normally distributed in the population.The table t value for this test 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 372 orders within 24 hours.Assuming $\alpha$ = 0.05,the appropriate decision is ___________________.

If the populations are normally distributed but the population variances are unknown the z-statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

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 _______.

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 __________.

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 ____________.

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.Claude's null 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 _______.

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

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 observed z 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 _______.

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.

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 _________________.

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

If the sample sizes are greater than 30 and the population variances are known,the basis for statistical inferences about the difference in two population means using two independent random samples is the z-statistic,regardless of the shapes of the population distributions.

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 _______.

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 ____.