Exam 10: Statistical Inferences About Two Populations

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 ___.

The difference in two sample means is normally distributed for sample sizes ≥ 30, only if 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 356 orders within 24 hours.Assuming $\alpha$ = 0.05, the appropriate decision is ___.

To determine if there is a difference in the strength of steel produced from two different production processes, a process manager will draw independent samples from the two processes and compare the difference in the sample means.

A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores.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 the treatment.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 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 ___.

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 ___.

Lucy Baker is analyzing demographic characteristics of two television programs, Lost (population 1)and Heroes (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 ___.

Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant.He wants to prove that Raymondville residents (population 1)dine out more often than Rosenberg residents (population 2).Denny commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 families 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 ___.

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 ___.

A researcher is interested in testing to determine if the mean of population one is greater than the mean of population two.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 items from population one resulting in a mean of 14.3 and a standard deviation of 3.4.He randomly selects a sample of 14 items from population two resulting in a mean of 11.8 and a standard deviation 2.9.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 ___.

A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores.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 the treatment.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 ___.

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 its 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 ___.

Lucy Baker is analyzing demographic characteristics of two television programs, Lost (population 1)and Heroes (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 ___.

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 its 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 ___.

Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant.He wants to prove that Raymondville residents (population 1)dine out more often than Rosenberg residents (population 2).Denny commissions a market survey to test this hypothesis.The market researcher used a random sample of 64 families 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 ___.

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 sample standard deviation (s)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 is interested in testing to determine if the mean of population one is greater than the mean of population two.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 items from population one resulting in a mean of 14.3 and a standard deviation of 3.4.He randomly selects a sample of 14 items from population two resulting in a mean of 11.8 and a standard deviation 2.9.He is using an alpha value of .10 to conduct this test.Assuming that the populations are normally distributed, the degrees of freedom for this problem are ___.

A statistician is being asked to test a new theory that the proportion of population A possessing a given characteristic is greater than the proportion of population B possessing the characteristic.A random sample of 600 from population A has been taken and it is determined that 480 possess the characteristic.A random sample of 700 taken from population B showed that 350 possess the characteristic.The observed z for this is ___.