Exam 10: Statistical Inferences About Two Populations

In order to construct an interval estimate for 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.

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.

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: 1 = 16 times per month and 2 = 14 times per month.Assume that $\sigma$ 1 = 4 and $\sigma$ 2 = 3.With $\alpha$ = .01,the appropriate decision is _____________.

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

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 __________. His alternative hypothesis 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 356 orders within 24 hours.Assuming $\alpha$ = 0.05,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,Tamara's alternate hypothesis is _______.

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.To obtain a 95% confidence interval,the table t value would be _______.

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 observed t value for this test 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 alternative hypothesis is _____________.

If a 98% confidence interval for the difference in the two population means does not contain zero,then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.02 level of significance.

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

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 ________.

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 observed z value 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 = 0.04 with n2 = 10.Assume that rod lengths are normally distributed in the population If $\alpha$ = 0.05,the observed F 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 and that the population variances are approximately equal.The critical t value used from the table for this 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 _______.

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.

.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,the critical t value from the table 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 _______.