Exam 10: Statistical Inferences About Two Populations

If the sample sizes are greater than 30 and the population variances are known,the basis for statistical inferences about the difference in two population means using two independent random samples is the z-statistic,regardless of the shapes of the population distributions.

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

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 _______.

When testing 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.) 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. Assuming a two-tail test and $\alpha$ = .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 null hypothesis 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 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.If $\alpha$ = 0.05,the critical F value 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 having 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 null hypothesis 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 _______.

Your company is evaluating two cloud-based,secured data storage services."Pie in the Sky," the newer service,claims its uploading and downloading speeds are faster than the older service,"Cloudy but Steady Skies." You need to make a decision based on published access times for both services at different times and for varying file sizes.Your 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.

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 372 orders within 24 hours. Assuming $\alpha$ = 0.05,the critical z value 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 90% confidence interval,the table t value would be _______.

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

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

If the populations are normally distributed and the variances of the two populations are not equal,it is appropriate to use the "unpooled" formula to determine the t-statistic for the hypothesis test of the difference in the two population means.

Your company is evaluating two cloud-based secured data storage services."Pie in the Sky," the newer service,claims its uploading and downloading speeds are faster than the older service,"Cloudy but Steady Skies." You need to make a decision based on published access times for both services at different times and for varying file sizes.To make your decision,you purchase a statistical study,which indicates that average download time for Pie in the Sky is 0.77 sec.per MB and for Cloudy but Steady Skies is 0.84.Assume that n₁ = n₂ = 50, $\sigma$ ₁ = 0.2 and $\sigma$ ₂ = 0.3.With $\alpha$ = .05,the appropriate decision is ______.

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 null hypothesis is ____________.