Exam 10: Statistical Inferences About Two Populations

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 appropriate decision is _________________.

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.The probability that the difference between the first sample proportion which possess the given characteristic and the second sample proportion which possess the given characteristic being more than +.03 is _______.

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.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 ___________.

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

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 observed F value 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.

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.Assuming a two-tail test and $\alpha$ = .05, the observed z value is _________________.

Collinsville Construction Company purchases steel rods for its projects.Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc.(population 1), and switching to Stockton Steel (population 2), since Stockton's rods had less variability in length.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 alternative hypothesis is _____________.

In a set of matched samples, each data value in one sample is related to or matched with a corresponding data value in the other sample.

In order to construct an interval estimate of 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.

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 individuals from each suburb, and reported the following: $\bar { x }$ ₁ = 16 times per month and $\bar { x }$ ₂ = 14 times per month.Assume that $\sigma$ ₁ = 4 and $\sigma$ ₂ = 3.With $\alpha$ = .01, 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 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 _______.

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 _______.

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.The standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion (used to calculate the z score)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.Maxwell's alternative hypothesis 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 from the table is ______.