Exam 10: Statistical Inferences About Two Populations

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 ___.

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 ___.

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,the observed F value 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.

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 ___.

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 critical F value 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.The point estimate of the difference in the population proportions is ___.

Test hypotheses and develop confidence intervals about the difference in two population proportions.

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 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 ___.

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 ___.

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 − 2)degrees of freedom.

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 ___.

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 plans to test this hypothesis using a random sample of 81 families from each suburb.His alternate hypothesis 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 6.Assume that stock prices are normally distributed in the population.Using $\alpha$ = 0.05,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 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 ___.

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 ___.

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 observed t value for this test 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 plans to test this hypothesis using a random sample of 81 families from each suburb.His null hypothesis is ___.