Exam 10: Statistical Inferences About Two Populations

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 appropriate decision 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.Assuming $\alpha$ = 0.01,the observed z 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.

Suppose that you can purchase a specialized electronic component from two providers.The electrical resistance of this component needs to be 0.15 ohms (Ω).Both providers offer components with a mean resistance of 0.15 Ω.You are interested in comparing the consistencies of both providers.To this end,you randomly select 15 components from the first provider and 18 from the second one.You can assume that the resistance is approximately normally distributed in the population.If you use a significance level of 0.10,the critical F value for this test is ______.

When finding a confidence interval for the difference between two population proportions we use the pooled estimate of the proportion.

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 _______.

The difference in two sample means is normally distributed for sample sizes ≥ 30,only if the populations are normally distributed.

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 observed z value is ______.

Suppose that .06 of each of two populations possess a given characteristic.Samples of size 400 are randomly drawn from each population.What is the probability that the differences in sample proportions will be greater than 0.02?

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 alternative hypothesis 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 _______.

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 observed F value 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 _________________.

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 _______.

The F statistic is a ratio of two independent sample variances.

You are evaluating investing in a cognitive training company.For this reason,you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem solving skills.You select a random sample of new users and get test scores for each participant in the sample.The test score is a composite of reading comprehension and problem solving skills.Two months later,you randomly select 15 users who have completed 75% or more of the recommended training for the last two months and have them take a test similar to the initial test.You are interested in determining whether the average test score before training is different than the average test score after training for this sample.The after-training average is 92.8,which is 2.7 points higher than the before-training average.The sample standard deviations of the differences is 1.2.You use a significance level of 0.10,and you can assume that the differences are normally distributed in the population.The table t-value for this test 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 appropriate decision 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.Assume that the differences are normally distributed in the population. The degrees of freedom for this test are _______.

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

In conducting a matched-pairs hypothesis test,the null and alternative hypotheses always represent one-tailed tests.