Exam 11: Asking and Answering Questions About the Difference Between Two Proportions

Would it be appropriate to use large sample hypothesis testing procedures for the following dataset? Why or why not? A random sample of 45 people was asked to indicate if they would return a lost wallet. Of the 45 sampled, 39 indicated that they would return the wallet.

A study by the Poultry Research Center seeks to determine if diet affects the onset of egg laying in juvenile Rhode Island Red hens. In a group of 34 hens that were fed scratch grain, 12 were laying eggs at 13 weeks of age. In a second, independent group of 25 hens that were fed on layer pellets, 4 hens were laying at 13 weeks of age. The 95% confidence interval for the difference in laying proportions at 13 weeks is: ​

A researcher would like to determine if the proportion of patients who indicate that they are happy with a hospital emergency room service is significantly different for those who receive treatment from a female nurse rather than a male nurse. As patients are admitted for treatment, they are randomly assigned to a nurse and prior to discharge are asked to indicate if they were happy or unhappy with the treatment they received. The following results were obtained: Female Nurse Male Nurse n = 35 n = 35 Number Happy: 21 Number Happy: 22 Find a 99% confidence interval for the difference of treatment proportions.

The P-value for a hypothesis test concerning the difference in two population proportions is always calculated by finding the area to the right of the test statistic, regardless of the alternative hypothesis.

The standard deviation of p₁ − p₂ used in the large sample test of p₁ − p₂ is the same as the standard deviation used in the large sample confidence interval for p₁ − p₂.

A 90% confidence interval for is (-0.05, -0.002). Which of the following is the 95% confidence interval calculated from the same data? ​

A researcher would like to determine if a higher proportion of students than faculty support caps on textbook prices. The researcher gathers a random sample of 500 students and 500 faculty members and asks whether or not they support textbook price caps. Of the 500 students, 378 say they support capping textbook prices and of the 500 faculty members 256 say they support capping prices. a.What are the hypotheses the researcher should use? b.Are the assumptions met for a large sample test? c.What is the P-value for the hypothesis test? d.What conclusion can be drawn?

To learn about the proportion of college students who are registered to vote, surveys were conducted in 2010 and in 2011. Suppose that in 2010, 39% of the people in a representative sample of 450 college students were registered to vote. In 2011, 33% of the people in a representative sample of 235 college students were registered to vote. For the 99% confidence level, determine the margin of error of the difference of the proportions. ​

A researcher would like to determine if the proportion of patients who indicate that they are happy with a hospital emergency room service is significantly different for those who receive treatment from a female nurse rather than a male nurse. As patients are admitted for treatment, they are randomly assigned to a nurse and prior to discharge are asked to indicate if they were happy or unhappy with the treatment they received. The following results were obtained: Female Nurse Male Nurse n = 35 n = 35 Number Happy: 21 Number Happy: 22 Perform a hypothesis test to determine if a significant difference exists.

A study is conducted to determine whether the proportion of airline passengers complaining with post-flight respiratory symptoms is larger for flights that do not circulate cabin air than for flights that do circulate the air. After checking to make sure that all of the necessary conditions were met, we calculated the value of the z test statistic to be z = 0.84. Which of the following is the P-value associated with this test? ​

An article describes a study of the effectiveness of a fabric device that acts like a support stocking for a weak or damaged heart. In the study, 88 people who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs plus surgery to install the stocking. After two years, 32% of the 41 patients receiving the stocking had improved, while 24% of the patients receiving the standard treatment had improved. Do these data provide evidence that the proportion of patients who improve is significantly higher for the experimental treatment than for the standard treatment? After checking to make sure that all of the necessary conditions were met, we calculated the value of the z test statistic to be z = 0.84. Which of the following is the P-value associated with this test?

A hotel chain is interested in evaluating reservation processes. Guests can reserve a room by using either a telephone system (T) or an online system (O) that is accessed through the hotel's web site. Independent random samples of 90 guests who reserved a room by phone and 68 guests who reserved a room online were selected. Of those who reserved by phone, 61 reported that they were satisfied with the reservation process. Of those who reserved online, 44 reported that they were satisfied. Based on these data, is it reasonable to conclude that the proportion who are satisfied is greater for those who reserve a room online? Which of the following hypotheses should be tested to answer this question? ​

When constructing a confidence interval for the difference of two population proportions, the appropriate standard error of is .

When testing hypotheses concerning differences in treatment effects from an experiment, the test statistic used for comparing two treatments is the same as the test statistic used for comparing differences between two population means from a sample study.

A marketing strategist would like to determine if a difference in the proportions of men and women who indicate "Action" as their favorite movie genre exists. The strategist gathers a random sample of 300 men and 200 women. Of the men, 156 indicate that "Action" is their favorite genre; of the women, 87 indicate that "Action" is their favorite. a.What are the hypotheses the researcher should use? b.Are the assumptions for a large sample test? c.What is the P-value for the hypothesis test? d.What conclusion can be drawn?

A group of people received the same treatment. Then the members of the initial group were randomly assigned to two new groups. Would the proportion of success be the same for the two groups? The variable represents the observed proportion for the group 1 and the variable represents the observed proportion for the group 2. What does it mean when the ? ​

In many animal societies, a role assumed by the adult male is a sentry, warning adult females and juveniles of approaching predators. Some students of animal behavior believe that in human society this role is active also. An interesting variation of this theory is that the human female accepts this role. In one 4-month study in Seattle, an investigator observed people crossing the street at an intersection with no traffic control. The observed behavior was the scanning behavior ("looking both ways") of adult males and females. The investigator reasoned that if the adult female accepted the protection of the adult male, the scanning rate when alone would be greater than when accompanied by an adult female. Data from this study is given below. Do these data support the investigator's hypothesis that the female scanning rate would be less when accompanied by a male? Assume that it is reasonable to regard these samples as representative of the corresponding populations. Provide statistical justification for your answer.

In many animal societies, a role assumed by the adult male is a sentry, warning adult females and juveniles of approaching predators. Some students of animal behavior believe that this occurs in human society also. In one 4-month study in Seattle an investigator observed people crossing the street at an intersection with no traffic control. The observed behavior was the scanning behavior ("looking both ways") of adult males and females. The investigator reasoned that if the adult male assumed a protective sentry role, the scanning rate when alone would be less than when accompanied by an adult female. Data from this study is given below. Do these data support the investigator's hypothesis that the male scanning rate would be greater when accompanied by a female? Assume that is reasonable to regard these samples as representative of the corresponding populations. Provide statistical justification for your answer.

A researcher would like to learn about the difference in proportions of students and faculty who support textbook price caps. The researcher gathers a random sample of 500 students and 500 faculty members and asks whether or not they support textbook price caps. Of the 500 students, 378 say they support capping textbook prices and of the 500 faculty members 256 say they support capping prices. a.Determine if the large sample confidence interval procedure can be used for estimation. b.Create a 95% confidence interval for the difference of the population proportions. c.Interpret the confidence interval.

For which of the following sample sizes and values would it be appropriate to use to estimate a difference in population proportions? ​ I. II. III. ​