## Statistics for Management

Statistics

## Quiz 15 :

Chi-Squared Tests

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Q49 Q49 Q49

Five types of apples are displayed side by side in several supermarkets in the city of Miami.It was noted that in one day, 180 customers purchased apples.Of these, 30 picked type A, 40 picked type B, 25 picked type C, 35 picked type D, and 50 picked type E.In Miami, can you conclude at the 5% significance level that there is a preferred type of apples?

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Q50 Q50 Q50

In 2011, the student body of a state university in Alabama consists of 30% freshmen, 25% sophomores, 27% juniors, and 18% seniors.A sample of 400 students taken from the 2012 student body showed that there are 138 freshmen, 88 sophomores, 94 juniors, and 80 seniors.Test with 5% significance level to determine whether the student body proportions have changed.

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Q51 Q51 Q51

In 2011, Brand A MP3 Players had 45% of the market, Brand B had 35%, and Brand C had 20%.This year the makers of brand C launched a heavy advertising campaign.A random sample of electronic stores shows that of 10,000 MP3 Players sold, 4,350 were Brand A, 3,450 were Brand B, and 2,200 were Brand C.Has the market changed? Test at = .01.

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Q52 Q52 Q52

Consider a multinomial experiment involving 100 trials and 3 categories (cells).The observed frequencies resulting from the experiment are shown in the accompanying table.
Use the 5% significance level to test the hypotheses H

_{0}: p_{1}= .45, p_{2}= .30, p_{3}= .25 vs.H_{1}: At least one proportion differs from their specified values.Free

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Q53 Q53 Q53

Consider a multinomial experiment involving 160 trials 4 categories (cells).The observed frequencies resulting from the experiment are shown in the accompanying table.
Use the 10% significance level to test the hypotheses: H

_{0}: p_{1}= p_{2}= p_{3}= p_{4}= .25 vs.H_{1}: At least one proportion differs from their specified values.Free

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Q54 Q54 Q54

A calculus professor posted the following grade distribution guidelines for her elementary calculus class: 8% A, 35% B, 40% C, 12% D, and 5% F.A sample of 100 elementary statistics grades at the end of last semester showed 12 As, 30 Bs, 35 Cs, 15 Ds, and 8 Fs.Test at the 5% significance level to determine whether the actual grades deviate significantly from the posted grade distribution guidelines.

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Q55 Q55 Q55

In 2011, computers of Brand A controlled 25% of the market, Brand B 20%, Brand C 10%, and brand D 45%.In 2015, sample data was collected from many randomly selected stores throughout the country.Of the 1,200 computers sold, 280 were Brand A, 270 were Brand B, 90 were Brand C, and 560 were Brand D.Has the market changed since 2011? Test at the 1% significance level.

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Q56 Q56 Q56

A cable company prepared four versions of a set of instructions for hooking up a TV.The company asked a sample of 1,600 people which one of the four forms was easiest to understand.In the sample, 425 people preferred Form A, 385 preferred Form B, 375 preferred Form C, and 415 preferred Form D.At the 5% level of significance, can one conclude that in the population there is a preferred form?

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Q59 Q59 Q59

A Deli proposes to serve 4 main Sandwiches.For planning purposes, the manager expects that the proportions of each that will be selected by her customers will be:
Of a random sample of 100 customers, 44 selected chicken, 24 selected roast beef, 13 selected Pastrami, and 10 selected tuna.Should the manager revise her estimates? Use = .01.

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Q61 Q61 Q61

Student Absenteeism
Consider a multinomial experiment involving n = 200 students of a large high school.The attendance department recorded the number of students who were absent during the weekdays.The null hypothesis to be tested is: H

_{0}: p_{1}= .10, p_{2}= .25, p_{3}= .30, p_{4}= .20, p_{5}= .15. -{Student Absenteeism Narrative} Test the hypothesis at the 5% level of significance with the following frequencies:Free

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Q62 Q62 Q62

Student Absenteeism
Consider a multinomial experiment involving n = 200 students of a large high school.The attendance department recorded the number of students who were absent during the weekdays.The null hypothesis to be tested is: H

_{0}: p_{1}= .10, p_{2}= .25, p_{3}= .30, p_{4}= .20, p_{5}= .15. -{Student Absenteeism Narrative} Test the hypothesis at the 5% level of significance with the following frequencies: (n = 100)Free

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Q63 Q63 Q63

Student Absenteeism
Consider a multinomial experiment involving n = 200 students of a large high school.The attendance department recorded the number of students who were absent during the weekdays.The null hypothesis to be tested is: H

_{0}: p_{1}= .10, p_{2}= .25, p_{3}= .30, p_{4}= .20, p_{5}= .15. -{Student Absenteeism Narrative} Test the hypothesis at the 5% level of significance with the following frequencies: (n = 50)Free

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Q64 Q64 Q64

Student Absenteeism
Consider a multinomial experiment involving n = 200 students of a large high school.The attendance department recorded the number of students who were absent during the weekdays.The null hypothesis to be tested is: H

_{0}: p_{1}= .10, p_{2}= .25, p_{3}= .30, p_{4}= .20, p_{5}= .15. -{Student Absenteeism Narrative} Review the previous results.What is the effect of decreasing the sample size?Free

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Q65 Q65 Q65

Sales Volumes
A telemarketer makes five calls per day.A sample of 200 days gives the frequencies of sales volumes listed below:
Assume the population is binomial distribution with a probability of purchase p equal to .50.
-{Sales Volumes Narrative} Compute the expected frequencies for x = 0, 1, 2, 3, 4, and 5 by using the binomial probability function or the binomial tables.Combine categories if necessary to satisfy the rule of five.

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Q66 Q66 Q66

Sales Volumes
A telemarketer makes five calls per day.A sample of 200 days gives the frequencies of sales volumes listed below:
Assume the population is binomial distribution with a probability of purchase p equal to .50.
-{Sales Volumes Narrative} Should the assumption of a binomial distribution be rejected at the 5% significance level?

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Q80 Q80 Q80

A chi-squared test of a contingency table with 6 degrees of freedom results in a test statistic of 13.25.Using the chi-squared table, the most accurate statement that can be made about the p-value for this test is that p-value is greater than .025 but smaller than .05.

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True False

Q106 Q106 Q106

The human resources manager of a consumer product company asked a random sample of employees how they felt about the work they were doing.The following table gives a breakdown of their responses by whether the employee is part time or full time (aka work status).Do the data provide sufficient evidence to conclude that the level of job satisfaction is related to their work status? Use = .10.

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Q107 Q107 Q107

The owner of a consumer products company asked a random sample of employees how they felt about the work they were doing.The following table gives a breakdown of their responses by age.Is there sufficient evidence to conclude that the level of job satisfaction is related to age? Use = .10.

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Q109 Q109 Q109

A major insurance firm interviewed a random sample of 1,200 college students to find out the type of life insurance preferred, if any.The results follow:
Is there evidence that life insurance preference of male students is different than that of female students? Test using the 5% level of significance.

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Q111 Q111 Q111

The Chairman of a committee has recently circulated pamphlets among the members, attempting to convince them that pension benefits should be the primary issue.A subsequent survey revealed the following breakdown of the members according to the plant at which they worked and the issue that they felt should be supported as the primary one.
Do the data indicate at the 5% significant level that there are differences between the two plants regarding which issue should be the primary one?

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Q112 Q112 Q112

Seat Belts
A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car.A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident.The data are shown in the table below.
-{Seat Belts Narrative} Which test would be used to properly analyze the data in this experiment?

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Q113 Q113 Q113

Seat Belts
A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car.A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident.The data are shown in the table below.
-{Seat Belts Narrative} State the appropriate null and alternative hypotheses for this experiment.

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Q114 Q114 Q114

Seat Belts
A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car.A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident.The data are shown in the table below.
-{Seat Belts Narrative} Prepare the table of expected values.

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Q115 Q115 Q115

Seat Belts
A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car.A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident.The data are shown in the table below.
-{Seat Belts Narrative} Calculate the value of the test statistic.

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Q116 Q116 Q116

Seat Belts
A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car.A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident.The data are shown in the table below.
-{Seat Belts Narrative} How many degrees of freedom are associated with the proper test in this experiment?

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Q117 Q117 Q117

Seat Belts
A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car.A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident.The data are shown in the table below.
-{Seat Belts Narrative} At 5% level of significance, what is the critical value of the test statistic?

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Q118 Q118 Q118

Seat Belts
A study was conducted to determine whether the use of seat belts in vehicles depends on whether or not a child was present in the car.A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained, and each person was classified according to (1) child present (yes/no) and (2) seat belt usage (worn or not worn) during the accident.The data are shown in the table below.
-{Seat Belts Narrative} At 5% level of significance, what is the proper conclusion?

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Q140 Q140 Q140

Suppose that two shipping companies, A and B, each decide to estimate the annual percentage of shipments on which a $100 or greater claim for loss or damage was filed by sampling their records, and they report the data shown below. The owner of Company B is hoping to use these data to show that her company is superior to Company A with regard to the percentage of claims filed.Which test would be used to properly analyze the data in this experiment?

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Multiple Choice

Q160 Q160 Q160

The null hypothesis states that the sample data came from a normally distributed population.The researcher calculates the sample mean and the sample standard deviation from the data.The data arrangement consisted of five categories.Using = .05, the appropriate critical value for this chi-squared test for normality is 5.99147.

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True False

Q162 Q162 Q162

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population.The researcher estimated the population mean and population standard deviation from a sample of 300 observations.In addition, the researcher used 6 standardized intervals to test for normality.Using a 2.5% level of significance, the critical value for this test is 14.4494.

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True False

Q163 Q163 Q163

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population.The researcher estimated the population mean and population standard deviation from a sample of 200 observations.In addition, the researcher used 5 standardized intervals to test for normality.Using a 10% level of significance, the critical value for this test is 4.60517.

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True False

Q166 Q166 Q166

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population.The researcher estimated the population mean and population standard deviation from a sample of 500 observations.In addition, the researcher used 6 standardized intervals to test for normality.Using a 5% level of significance, the critical value for this test is:

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Multiple Choice

Q173 Q173 Q173

The following data are believed to have come from a normal probability distribution.
The mean of this sample equals 26.80, and the standard deviation equals 6.378.Use the goodness-of-fit test at the 5% significance level to test whether the data indeed come from a normal distribution.

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Q174 Q174 Q174

Suppose that a random sample of 60 observations was drawn from a population.After calculating the mean and standard deviation, each observation was standardized and the number of observations in each of the intervals below was counted.Can we infer at the 10% significance level that the data were drawn from a normal population?

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Q175 Q175 Q175

Suppose that a random sample of 150 observations was drawn from a population.After calculating the mean and standard deviation, each observation was standardized and the number of observations in each of the intervals below was counted.Can we infer at the 5% significance level that the data were drawn from a normal population?

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