Exam 10: Statistical Inferences About Two Populations

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 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 _______.

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.What is the probability that the differences in sample proportions will be greater than 0.02?

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 ___________________.

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 appropriate decision 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 observed F value is ___________.

In conducting a matched-pairs hypothesis test,the null and alternative hypotheses always represent one-tailed tests.

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

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 degrees of freedom in this problem are _______.

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 null hypothesis is _______.

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

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.The point estimate of the difference in the population proportions is _______.

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

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 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 _______.

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

If a 90% confidence interval for the difference in the two population means contains zero,then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.

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 _______.

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 _________.

Hypothesis tests conducted on sets of matched samples are sometimes referred to as correlated t tests.