Exam 10: Statistical Inference Concerning Two Populations

The student senate at a local university is about to hold elections.A representative from the women's sports program and a representative from the men's sports program must both be elected.Two candidates,an incumbent and a challenger,are vying for each position and early polling results are presented next.A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates.In a sample of 100 voters,67 said that they would vote for the women's incumbent candidate.In a separate sample of 100 voters,55 said they would vote for the men's incumbent candidate.Let p₁ and p₂ be the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs,respectively.Which of the following is the correct conclusion for the test at = 0.05?

In August 2010,Massachusetts enacted a 150-day right-to-cure period that mandates that lenders give homeowners who fall behind on their mortgage an extra five months to become current before beginning foreclosure proceedings.Policymakers claimed that the policy would result in a higher proportion of delinquent borrowers becoming current on their mortgages.To test this claim,researchers took a sample of 244 homeowners in danger of foreclosure in the time period surrounding the enactment of this law.Of the 100 who fell behind just before the law was enacted,30 were able to avoid foreclosure,and of 144 who fell behind just after the law was enacted,48 were able to avoid foreclosure.Let p₁andp₂ represent the proportion of delinquent borrowers who avoid foreclosure just before and just after the right-to-cure law is enacted,respectively.Which of the following is the correct competing hypotheses that will test the policymakers' claim?

A bank is trying to determine which model of safe to install.The bank manager believes that each model is equally resistant to safe crackers but sets up a test to be sure.He hires nine safe experts to break into each of the models,timing each endeavor.The results (in seconds)are given next,paired by expert.Let D be the difference: Time to break Safe 1 minus Time to break Safe 2. Which of the following hypotheses will determine if the two safes take,on average,the same amount of time to crack?

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 appropriate conclusion at the 5% significance level?

Two or more random samples are considered independent if _________ .

Which of the following is not a restriction for comparing two population means?

Which of the following is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling.

The serious delinquency rate measures the proportion of homes that are well behind on their mortgage payments.A real estate investor is trying to decide in which of two neighborhoods in Phoenix to buy an investment property.He is trying to decide if the serious delinquency rate differs between the two neighborhoods.He took a sample of 70 homes in neighborhood 1 and found 14 homes were seriously delinquent.He took a sample of 80 homes in neighborhood 2 and 10 homes were seriously delinquent. a.Specify the competing hypotheses to determine if the delinquency rates in the two neighborhoods are equal. b.Calculate the value of the test statistic and the p-value. c.Make a conclusion at the 10% significance level.How should the delinquency rate influence the investor's decision?

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 is the correct value of the test statistics?

A Catholic priest believes that a higher proportion of women in his congregation regularly attend services than the men in his congregation.He randomly selects 100 men and 100 women from his congregation and finds that 32 men and 48 women regularly attend. a.Specify the competing hypotheses to test the priest's claim. b.Calculate the value of the relevant test statistic. c.Compute the p-value.Does the evidence support the priest's claim at the 1% significance level?

You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood.Let women and men be represented by populations 1 and 2,respectively.Which of the following hypotheses is relevant to this claim?

If the underlying populations cannot be assumed to be normal,then by the central limit theorem,the sampling distribution of is approximately normal only if the sum of the sample observations is sufficiently large-that is,when

A veterinarian wants to know if pit bulls or golden retrievers have a higher incidence of tooth decay at the age of three.The veterinarian surveys 120 three-year-old pit bulls and finds 30 of them have tooth decay.The veterinarian then surveys 160 three-year-old golden retrievers and finds 32 of them have tooth decay.Number the population of pit bulls and golden retrievers by 1 and 2,respectively.At the 10% significance level,can the veterinarian conclude the proportion of pit bulls that have tooth decay is different than the proportion of golden retrievers that have tooth decay?

Assume the competing hypotheses take the following form: H₀: µ₁- µ₂ = 0,H_A: µ₁- µ₂ ≠ 0,where µ₁ is the population mean for population 1 and µ₂ is the population mean for population 2.Also assume that the populations are normally distributed and that the observations in the two samples are independent.The population variances are not known but are assumed equal.Which of the following expressions is appropriate test statistic?

When comparing two population means,their hypothesized difference _________ .

A computer manufacturer believes that the proportion of hardware malfunctions is different in humid climates than in dry climates.To test this claim,the manufacturer takes a random sample of 400 machines sold in Florida (humid)and 400 machines sold in Arizona (dry).The manufacturer finds that 44 of the machines in Florida and 24 of the machines in Arizona had hardware malfunctions. a.Specify the competing hypotheses to test the manufacturer's claim. b.Calculate the value of the relevant test statistic. c.Compute the p-value.Does the evidence support the computer manufacturer's claim at the 10% significance level?

Students are planning a bake sale to raise money to purchase new uniforms for the volleyball team at a local high school.They would like to generate the best possible results and have therefore been experimenting with cupcake recipes.Nine different recipes are chosen and baked.The same recipes with 50% additional baking powder are then baked,leaving all other aspects of the recipe unchanged.They then measured the height of the cupcakes paired by recipe.The sample mean of the difference " with a sample standard deviation of ".Perform a hypothesis test at the 1% level of significance to determine if the height of cupcakes rises with the additional baking powder.Assume the distribution of cupcake heights is normally distributed.

A common case of dependent sampling is usually referred to as __________ sampling.

A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season.The first variety is milk chocolate while the second is milk chocolate filled with mint.It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances.Two independent samples of 18 observations each are collected for the holiday period.A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2.5 million.A sample mean of 13.5 million truffles filled with mint sold with a sample standard deviation of 2.3 million.Use milk chocolate as population 1 and mint chocolate as population 2.Which of the following are the appropriate hypotheses to determine if the average sales of the two varieties of truffles differ significantly during the holiday season?

Which of the following set of hypotheses is used to test if the mean of the first population is smaller than the mean of the second population,using matched-paired sampling?