Exam 12: Hypothesis Testing for Two Populations

A researcher believes a new diet should improve weight gain. To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected. The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds. Assume that the values are normally distributed in each population and that the population variances are approximately equal. Using $\alpha$ = 0.05, the observed 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 large corporation wants to determine whether or not the typing efficiency course given at a local college has any influence on typing speed of secretaries. A sample of 6 secretaries is selected, and they are sent to take the course. The typing speed of the secretaries in word per minute (WPM) are shown below: At , test if it can be concluded that taking the course increased the typing speed of the secretaries?

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 ___.

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 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 level of significance is selected to be 0.10. If a two-tailed test is performed, the null hypothesis would be rejected if the observed value of t is ___.

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 $\textbf{ not }$ 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 and that the population variances are approximately equal, the degrees of freedom for this problem are ___.

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 ___.

If the variances of the two populations are $\textbf{ not }$ 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.

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 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_d) of the differences 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 degrees of freedom in this problem are ___.

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 $\textbf{ not }$ 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 ___.

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 $\sigma$ ₁ = 0.2 and $\sigma$ ₂ = 0.3. With $\alpha$ =.05, the critical z value 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 372 orders within 24 hours. Assuming $\alpha$ = 0.05, the observed z 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. Assuming $\alpha$ = 0.01, 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 ___.

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 ___.

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

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 ___.