Exam 12: Hypothesis Testing for Two Populations

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 ___.

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.

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. With a two-tail test and $\alpha$ =.05, the appropriate decision 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 ___.

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 ___.

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 ___.

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 appropriate decision is ___.

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.

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. With a two-tail test and $\alpha$ =.05, the critical z values are ___.

A university administrator believes that business students are more likely to be working and going to school than their liberal arts majors. This information may lead to the business school offering courses in the evening hours while the liberal arts college maintains a daytime schedule. To test this theory the proportion of business students who are working at least 20 hours per week is compared to the proportion of liberal arts students who are working at least 20 hours per week. A random sample of 600 from the business school has been taken and it is determined that 480 students work at least 20 hours per week. A random sample of 700 liberal arts students showed that 350 work at least 20 hours per week. The observed z for this 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 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. Maureen's alternative hypothesis is ___.

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

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 individuals from each suburb, and reported the following: ₁ = 16 times per month and ₂ = 14 times per month. Assume that $\sigma$ ₁ = 4 and $\sigma$ ₂ = 3. With $\alpha$ =.01, the appropriate decision is ___.

You are interested in determining the difference in two population means. You select a random sample of 8 items from the first population and 8 from the second population and then compute a 95% confidence interval. The sample from the first population has an average of 12.2 and a standard deviation of 0.8. The sample from the second population has an average of 11.7 and a standard deviation of 1.0. Assume that the values are normally distributed in each population and that the population variances are approximately equal. The corresponding critical t 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 critical z value is ___.

When testing for the difference between two population proportions, we use the "pooled" estimate of the proportion.

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 ___.

You are interested in determining whether the mean price of electricity offered by solar companies is different in the southern states than in the northern states. You select a random sample of 8 solar companies from the southern states and 11 from the northern states. For the southern states, the average price is 12.2 cents per kWh (kilowatt hour) and the standard deviation is 0.8 cents per kWh. For the northern states, the average and standard deviation are 11.7 and 1.0 cents per kWh respectively. If you use a significance level α = 0.10 and assuming the values are normally distributed in both populations, the critical t 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 ___.