Probability and Statistics

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For questions 6 - 10 use the chi-squared distribution to test the hypothesis.

6) A restaurant owner wants to see if the business is good enough for him to purchase a restaurant. He asks the present owner for a breakdown of how many customers that come in for lunch each day and the results are as follows: Monday - 20, Tuesday - 30, Wednesday - 25, Thursday - 40 and Friday - 55. The prospective owner observes the restaurant and finds the following number of customers coming for lunch each day: Monday- 30, Tuesday - 15, Wednesday- 7, Thursday 40, and Friday - 33. At a 95% confidence level determine whether the present owner reported the correct number of customers for lunch each day.

7) An employer polled its employers to see if they agree with the proposed new store hours and whether or not their present shift made a difference in their answers. The customers answered 1 for agree, 2 for don't know, and 3 for disagree. Nine first shift employees answered "agree", 15 second shift employees answered "agree", and 20 third shift employees answered agree. With a 95% confidence level determine whether or not the employees' present shift played a role in their responses to the poll.

8) A politician surveyed 100 citizens to determine if their job title had anything to do with the way they responded to the following statement: "A city-wide curfew will be put into place. Select the time that you think it should be put into place. 8pm, 9pm, or 10pm". He is mostly concerned with the 10 pm responses. 25 teachers chose 10pm, 40 doctors chose 10pm, and 35 police responded 10pm. With a 95% confidence level, determine whether job title plays a role in how the citizens responded to the statement.

9) A meter reader did an experiment to see if there is a relationship between the number of tickets she writes and the number of blocks she is away from the park that is considered the heart of the city. At 0 blocks from the park she writes 35 tickets, at 1 block away from the park she writes 25 tickets, at 2 blocks from the park she writes 20 tickets and at 3 blocks from the park she writes 25 tickets. Use a 95% confidence level.

10) A high school principal asks his students to respond to the following statement: "School should start at 9:00am rather than 7:00am. Answer 1 for agree, 2 for don't know, and 3 for disagree." There were 90 seniors who answered agree, 35 juniors, 30 sophomores, and 25 freshmen. Help the principal decide with a 95% confidence level that the students' status played a role in how they responded to the question.

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    7)  An employer polled its employers to see if they agree with the proposed new store hours and whether or not their present shift made a difference in their answers.  The customers answered 1 for agree, 2 for don't know, and 3 for disagree.  Nine first shift employees answered "agree", 15 second shift employees answered "agree", and 20 third shift employees answered agree.  With a 95% confidence level determine whether or not the employees' present shift played a role in their responses to the poll.

    DF: 3.841

    X2: 20.54+20.54=41.08 

    41.08 > 3.841

    We must reject the null hypothesis that the employees present shift played a role in the responses to the poll.

    8)  A politician surveyed 100 citizens to determine if their job title had anything to do with the way they responded to the following statement:  "A city-wide curfew will be put into place.  Select the time that you think it should be put into place.  8pm, 9pm, or 10pm".  He is mostly concerned with the 10 pm responses.  25 teachers chose 10pm, 40 doctors chose 10pm, and 35 police responded 10pm.  With a 95% confidence level, determine whether job title plays a role in how the citizens responded to the statement.

    DF: 5.991

    X2: 3.5034

    5.991 > 3.5034 

    We can not reject the null hypothesis that job title plays a role in how the citizens responded to the statement about curfew change. 

    9)  A meter reader did an experiment to see if there is a relationship between the number of tickets she writes and the number of blocks she is away from the park that is considered the heart of the city.  At 0 blocks from the park she writes 35 tickets, at 1 block away from the park she writes 25 tickets, at 2 blocks from the park she writes 20 tickets and at 3 blocks from the park she writes 25 tickets.  Use a 95% confidence level.

    (35-26.25)²26.25+ (25-26.25)²26.25+(20-26.25)²26.25+(25-26.25)²26.25= 2.92+ .059+ 1.49+.059=4.52

    95% confidence level = .05 with 3 degrees of freedom = 7.82

    X² = 4.52  and 4.52 < 7.82

    We must fail to reject the null hypothesis and conclude that there is no relationship between the number of tickets she writes and the number of blocks she is away from the park that is considered the heart of the city.


    10)  A high school principal asks his students to respond to the following statement:  "School should start at 9:00am rather than 7:00am.  Answer 1 for agree, 2 for don't know, and 3 for disagree."  There were 90 seniors who answered agree, 35 juniors, 30 sophomores, and 25 freshmen.  Help the principal decide with a 95% confidence level that the students' status played a role in how they responded to the question.

    DF: 7.82

    X2: 28.92

    28.92 > 7.82

    We must reject the null hypothesis that the students' status played a role in how they responded to the question. 

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