In a psychology experiment, 140 students were divided into

Each of two comparable classes of 15 students responded to two different methods of instructions, giving the following scores on a standardized test: Use a chi-square test with \(\alpha=0.05\) to test the equality of the distributions of test scores by dividing the combined sample into three equal parts (low, middle, high). Equation Transcription: Text Transcription: alpha=0.05

We wish to see if two groups of nurses distribute their time in six different categories about the same way. That is, the hypothesis under consideration is \(H_{0}: p_{i 1}=\) \(p_{i 2}, i=1,2, \ldots, 6\). To test this hypothesis, nurses are observed at random throughout several days, each observation resulting in a mark in one of the six categories. A summary of the results is given by the following frequency table: Use a chi-square test with \(\alpha=0.05\). Equation Transcription: Text Transcription: H_0:p_i1= p_i2,i=1,2,,6 alpha=0.05

Suppose that a third group of nurses was observed along with groups I and II of Exercise 9.2-1, resulting in the respective frequencies \(130,75,136,33,61\), and \(65\) . Test \(H_{0}: p_{i 1}=p_{i 2}=p_{i 3}, i=1,2, \ldots, 6\), at the \(\alpha=0.025\) significance level. Equation Transcription: Text Transcription: 130,75,136,33,61 65 H_0:p_i1=p_i2=p_i3,i=1,2,,6 alpha=0.025

A study was conducted to determine the media credibility for reporting news. Those surveyed were asked to give their age, gender, education, and the most credible medium. The results of the survey are as follows: (a) Test whether media credibility and age are independent. (b) Test whether media credibility and gender are independent. (c) Test whether media credibility and education are independent. (d) Give the approximate \(p\)-value for each test. Equation Transcription: Text Transcription: p

In the following contingency table, 1015 individuals are classified by gender and by whether they favor, oppose, or have no opinion on a complete ban on smoking in public places: Test the null hypothesis that gender and opinion on smoking in public places are independent. Give the approximate \(p\)-value of this test. Equation Transcription: Text Transcription: p

A student who uses a certain college’s recreational facilities was interested in whether there is a difference between the facilities used by men and those used by women. Use \(\alpha=0.05\) and the following data to test the null hypothesis that facility and gender are independent attributes: Equation Transcription: Text Transcription: alpha=0.05

One hundred music majors in a random sample were classified as follows by gender and by the kind of instrument (including voice) that they played: Test whether the selection of instrument is independent of the gender of the respondent. Approximate the \(p\)-value of this test. Equation Transcription: Text Transcription: p

A survey of high school girls classified them by two attributes: whether or not they participated in sports and whether or not they had one or more older brothers. Use the following data to test the null hypothesis that these two attributes of classification are independent: Approximate the \(p\)-value of this test. Do we reject the null hypothesis if \(\alpha=0.05\)? Equation Transcription: Text Transcription: p alpha=0.05

A random sample of 50 women who were tested for cholesterol was classified according to age and cholesterol level and grouped into the following contingency table. Test the null hypothesis \(H_{0}\): Age and cholesterol level are independent attributes of classification. What is your conclusion if \(\alpha=0.01\)? Equation Transcription: Text Transcription: H_0 alpha=0.01

In a psychology experiment, 140 students were divided into majors emphasizing left-hemisphere brain skills (e.g., philosophy, physics, and mathematics) and majors emphasizing right-hemisphere skills (e.g., art, music, theater, and dance). They were also classified into one of three groups on the basis of hand posture (right non-inverted, left inverted, and left non-inverted). The data are as follows: Do these data show sufficient evidence to reject the claim that the choice of college major is independent of hand posture? Let \(\alpha=0.025\). Equation Transcription: Text Transcription: p alpha=0.025

Although high school grades and testing scores, such as SAT or ACT, can be used to predict first-year college grade-point average (GPA), many educators claim that a more important factor influencing GPAis the living conditions of students. In particular, it is claimed that the roommate of the student will have a great influence on his or her grades. To test this hypothesis, suppose we selected at random 200 students and classified each according to the following two attributes: (a) Ranking of the student’s roommate on a scale from 1 to 5, with 1 denoting a person who was difficult to live with and discouraged scholarship, and 5 signifying a person who was congenial and encouraged scholarship. (b) The student’s first-year GPA. Say this classification gives the following \(5 \times 4\) contingency table: Compute the chi-square statistic used to test the independence of the two attributes, and compare it with the critical value associated with \(\alpha=0.05\). Equation Transcription: Text Transcription: 5x4 alpha=0.05

A random survey of 100 students asked each student to select the most preferred form of recreational activity from five choices. Following are the results of the survey: Test whether the choice is independent of the gender of the respondent. Approximate the \(p\)-value of the test. Would we reject the null hypothesis at \(\alpha=0.05\)? Equation Transcription: Text Transcription: alpha=0.05 p

Suppose that a third class \((W)\) of 15 students was observed along with classes \(U\) and \(V\) of Exercise 9.2-3, resulting in scores of Again, use a chi-square test with \(\alpha=0.05\) to test the equality of the three distributions by dividing the combined sample into three equal parts. Equation Transcription: Text Transcription: (W) U V alpha=0.05

We wish to see if two groups of nurses distribute their time in six different categories about the same way. That is, the hypothesis under consideration is H0: pi1 = pi2, i = 1, 2, ... , 6. To test this hypothesis, nurses are observed at random throughout several days, each observation resulting in a mark in one of the six categories. A summary of the results is given by the following frequency table: Category 1 2 3 4 5 6 Totals Group I 95 36 71 21 45 32 300 Group II 53 26 43 18 32 28 200 Use a chi-square test with = 0.05.

Suppose that a third group of nurses was observed along with groups I and II of Exercise 9.2-1, resulting in the respective frequencies 130, 75, 136, 33, 61, and 65. Test H0: pi1 = pi2 = pi3, i = 1, 2, ... , 6, at the = 0.025 significance level.

Each of two comparable classes of 15 students responded to two different methods of instructions, giving the following scores on a standardized test: Class U: 91 42 39 62 55 82 67 44 51 77 61 52 76 41 59 Class V: 80 71 55 67 61 93 49 78 57 88 79 81 63 51 75 Use a chi-square test with = 0.05 to test the equality of the distributions of test scores by dividing the combined sample into three equal parts (low, middle, high)

Suppose that a third class (W) of 15 students was observed along with classes U and V of Exercise 9.2-3, resulting in scores of 91 73 67 83 59 98 87 69 78 80 65 94 82 74 85 Again, use a chi-square test with = 0.05 to test the equality of the three distributions by dividing the combined sample into three equal parts.

In the following contingency table, 1015 individuals are classified by gender and by whether they favor, oppose, or have no opinion on a complete ban on smoking in public places: Smoking in Public Places Gender Favor Oppose No Opinion Totals Male 262 231 10 503 Female 302 205 5 512 Totals 564 436 15 1015 Test the null hypothesis that gender and opinion on smoking in public places are independent. Give the approximate p-value of this test

A random survey of 100 students asked each student to select the most preferred form of recreational activity from five choices. Following are the results of the survey: Recreational Choice Baseball Jogging Gender Basketball Softball Swimming Running Tennis Totals Male 21 5 9 12 13 60 Female 9 3 1 15 12 40 Totals 30 8 10 27 25 100 Test whether the choice is independent of the gender of the respondent. Approximate the p-value of the test. Would we reject the null hypothesis at = 0.05?

One hundred music majors in a random sample were classified as follows by gender and by the kind of instrument (including voice) that they played:Instrument Gender Piano Woodwind Brass String Vocal Totals Male 4 11 15 6 9 45 Female 7 18 6 6 18 55 Totals 11 29 21 12 27 100 Test whether the selection of instrument is independent of the gender of the respondent. Approximate the p-value of this test.

A student who uses a certain colleges recreational facilities was interested in whether there is a difference between the facilities used by men and those used by women. Use = 0.05 and the following data to test the null hypothesis that facility and gender are independent attributes: Facility Racquetball Gender Court Track Totals Male 51 30 81 Female 43 48 91 Totals 94 78 172

A survey of high school girls classified them by two attributes: whether or not they participated in sports and whether or not they had one or more older brothers. Use the following data to test the null hypothesis that these two attributes of classification are independent: Participated in Sports Older Brother(s) Yes No Totals Yes 12 8 20 No 13 27 40 Totals 25 35 60 Approximate the p-value of this test. Do we reject the null hypothesis if = 0.05?

A random sample of 50 women who were tested for cholesterol was classified according to age and cholesterol level and grouped into the following contingency table. Cholesterol Level Age <180 180210 >210 Totals <50 5 11 9 25 50 4 3 18 25 Totals 9 14 27 50 Test the null hypothesis H0: Age and cholesterol level are independent attributes of classification. What is your conclusion if = 0.01?

Although high school grades and testing scores, such as SAT or ACT, can be used to predict first-year college grade-point average (GPA), many educators claim that a more important factor influencing GPA is the living conditions of students. In particular, it is claimed that the roommate of the student will have a great influence on his or her grades. To test this hypothesis, suppose we selected at random 200 students and classified each according to the following two attributes: (a) Ranking of the students roommate on a scale from 1 to 5, with 1 denoting a person who was difficult to live with and discouraged scholarship, and 5 signifying a person who was congenial and encouraged scholarship. (b) The students first-year GPA. Say this classification gives the following 54 contingency table: Grade-Point Average Rank of Under Roommate 2.00 2.002.69 2.703.19 3.204.00 Totals 1 8 9 10 4 31 2 5 11 15 11 42 3 6 7 20 14 47 4 3 5 22 23 53 5 1 3 11 12 27 Totals 23 35 78 64 200 Compute the chi-square statistic used to test the independence of the two attributes, and compare it with the critical value associated with = 0.05.

In a psychology experiment, 140 students were divided into majors emphasizing left-hemisphere brain skills (e.g., philosophy, physics, and mathematics) and majors emphasizing right-hemisphere skills (e.g., art, music, theater, and dance). They were also classified into one of three groups on the basis of hand posture (right noninverted, left inverted, and left noninverted). The data are as follows: LH RH RN 89 29 LI 5 4 LN 5 8 Do these data show sufficient evidence to reject the claim that the choice of college major is independent of hand posture? Let = 0.025.

A study was conducted to determine the media credibility for reporting news. Those surveyed were asked to give their age, gender, education, and the most credible medium. The results of the survey are as follows: (a) Test whether media credibility and age are independent. (b) Test whether media credibility and gender are independent. (c) Test whether media credibility and education are independent. (d) Give the approximate p-value for each test.