Exam 10: Statistical Inference Concerning Two Populations

There is only one type of matched-pairs sampling.

A shoe company designed a low-top and high-top version of a particular shoe.One of the shoe-making engineers claims that the low-top version does not last as long as the high-top version before wearing out.To test this claim,she takes a sample of 36 low-top and 64 high-top wearers and asks each the length of time before their shoes wore out.She finds that the low-tops wore out in an average of 140 days,and the high-tops wore out in an average of 150 days.Suppose the population standard deviation for both is 20 days. a.Specify the competing hypotheses to determine whether high-tops last longer than low-tops for this particular shoe. b.Calculate the value of the relevant test statistic. c.Compute the p-value.Does the evidence support the commentator's claim at the 1% significance level?

Calcium is an essential nutrient for strong bones and for controlling blood pressure and heart beat.Because most of the body's calcium is stored in bones and teeth,the body withdraws the calcium it needs from the bones.Over time,if more calcium is taken out of the bones than is put in,the result may be thin,weak bones.This is especially important for women who are often recommended a calcium supplement.A consumer group activist assumes that calcium content in two popular supplements are normally distributed with the same unknown population variance,and uses the following information obtained under independent sampling: Let μ₁ and μ₂ denote the corresponding population means.Can we conclude that the average calcium content of the two supplements differs at the 95% confidence level?

The hypothesis test H₀: p₁- p₂≤ d₀;H_A: p₁- p₂> d₀ is a left-tailed test.

A university wants to compare out-of-state applicants' mean SAT math scores (μ₁)to in-state applicants' mean SAT math scores (μ₂).The university looks at 35 in-state applicants and 35 out-of-state applicants.The mean SAT math score for in-state applicants was 540,with a standard deviation of 20.The mean SAT math score for out-of-state applicants was 555,with a standard deviation of 25.It is reasonable to assume the corresponding population standard deviations are equal.To calculate the confidence interval for the difference μ₁ - μ₂,what is the number of degrees of freedom of the appropriate probability distribution?

What type of data should be collected when examining a situation in which two candidates running in different elections are being compared in their likelihood of winning their elections?

A bicycle manufacturer makes downhill mountain bikes out of two different types of material: carbon fiber and aluminum.One test the company uses to measure the durability of their frames is called a stress test.The company tested 10 aluminum and 10 carbon frames to see how many stress cycles each type of material could withstand before breaking.The results are listed next in thousands.It is not reasonable to assume equal population variances.Assume the number of stress cycles a bicycle frame can withstand before breaking is normally distributed. a.Specify the competing hypotheses to determine if a carbon frame can withstand at least 10,000 more stress cycles than an aluminum frame. b.Calculate the value of the test statistic and its p-value.c.Make a conclusion at the 5% significance level.

A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights.The magazine surveyed Standard Air (population 1)and Down Under airlines (population 2).Standard Air lost 45 out of 600 bags.Down Under airlines lost 30 of 500 bags.Does Standard Air have a higher population proportion of lost bags on international flights? Which of the following is the correct competing hypotheses?

A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening.Two independent samples of 25 weeks are collected for Tuesday and Wednesday.The mean attendance on Tuesday evening is calculated as 5,500,while the mean attendance on Wednesday evening is calculated as 5,850.The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445.What are the appropriate hypotheses to determine whether there is a difference in attendance for shows on Tuesday evening and Wednesday evening? Use Tuesday attendance as population 1 mean μ₁ and Wednesday attendance as population 2 mean μ₂,or μ_D as the mean difference in matched-pairs sampling.

A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males.Suppose 250 females and 200 males responded to the study.Which of the following are an appropriate null and alternative hypotheses to test whether the proportion of females suffering from asthma is greater than the proportion of males?

A left-tailed test determines whether μ₁is _____ then μ₂.

The t statistic is used to estimate the difference between two population proportions.

We use the difference between the sample proportions as the point estimator of the difference between two population proportions .

According to a recent survey,women chat on their mobile phones more than do men (CNN.com,August 25,2010).Irina wants to estimate the difference between the average chat time for female and male college students.She takes a random sample of 40 male students and 40 female students in her college.She finds that female students chatted for a sample average of 820 minutes per month with a sample standard deviation of 160 minutes.Male students,on the other hand,chatted for a sample average of 760 minutes per month with a sample standard deviation of 240 minutes.You may assume that the population variances are equal. a.Construct a 95% confidence interval for the difference between the population means. b.Can we conclude that average chat time is different between female and male college students with 95% confidence?

To use Excel for solving hypothesis tests for the mean difference you should choose: Data > __________ > t-Test: Paired Two Sample for Means options.

According to a recent survey,women chat on their mobile phones more than do men (CNN.com,August 25,2010).To determine if the same patterns also exist in colleges,Irina takes a random sample of 40 male students and 40 female students in her college.She finds that female students chatted for a sample average of 820 minutes per month,with a sample standard deviation of 160 minutes.Male students,on the other hand,chatted for a sample average of 760 minutes per month,with a sample standard deviation of 240 minutes.It is not reasonable to assume equal population variances. a.Specify the competing hypotheses to determine if female students chat more,on average,than male students. b.Calculate the value of the test statistic and its p-value.c.Make a conclusion at the 5% significance level.

A new study has found that,on average,6- to 12-year-old children are spending less time on household chores today compared to 1981 levels.Suppose two samples representative of study's results report the following summary statistics for the two periods. 1981 Levels 2008 Levels 30 minutes 24 minutes S₁ = 4.2 minutes S₂ = 3.9 minutes N₁ = 30 N₂ = 30 Using a 5% confidence level,which of the following is correct?

A candidate in a local election thinks seniors are by far her best supporters.She believes that the difference in the support between seniors and nonseniors is more than 15%.To verify this belief,the team samples 100 seniors and 150 nonseniors to find what proportion of each group supports the candidate.It is found that 50 of the seniors support her and 36 of the nonseniors support her. a.Specify the hypotheses to determine if the difference in the support between seniors and nonseniors is more than 15%. b.Calculate the value of the test statistic and the p-value. c.Make a conclusion at the 5% significance level.

The same formulas are used to compute test statistic when the hypothesized difference between population proportions is zero or not.

A farmer uses a lot of fertilizer to grow his crops.The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does.He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch.Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch.Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch,respectively.Assume the distribution of nitrogen in fertilizer is normally distributed.Let µ1and µ2 represent the average amount of nitrogen per batch for fertilizer's A and B,respectively.Which of the following is an appropriate p-value?