STAT 200 Week 8 Homework

  1. STAT 200 Week 8 Homework
    Lane – Ch. 15
    10. If an experiment is conducted with 5 conditions and 6 subjects in each condition, what are dfn and dfe?
    17. The following data are from a hypothetical study on the effects of age and time on scores on a test of reading comprehension. Compute the analysis of variance summary table.

    12-year-olds 16-year-olds
    30 minutes 66 74
    68 71
    59 67
    72 82
    46 76
    60 minutes 69 95
    61 92
    69 95
    73 98
    61 94

    Illowsky – Ch. 13
    Use the following information to answer the next three exercises. Suppose a group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.

    Northeast South West Central East
    16.3 16.9 16.4 16.2 17.1
    16.1 16.5 16.5 16.6 17.2
    16.4 16.4 16.6 16.5 16.6
    16.5 16.2 16.1 16.4 16.8
    x-bar = ________ ________ ________ ________ ________
    s^2 = ________ ________ ________ ________ ________
    Hα: At least any two of the group meansµ1,µ2, …,µ5are not equal.

    61. degrees of freedom – numerator: df(num) = ________
    63. F static = ________
    69. A researcher wants to know if the mean times (in minutes) that people watch their favorite news station are the same. Suppose that Table 13.24 shows the results of a study.
    CNN  FOX  Local
    45    15    72
    12    43    37
    18    68    56
    38    50    60
    23    31    51
    35    22      ?
    Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.
    71. Are the mean number of times a month a person eats out the same for whites, blacks, Hispanics and Asians? Suppose that Table 13.26 shows the results of a study.

    White Black Hispanic Asian
    6 4 7 8
    8 1 3 3
    2 5 5 5
    4 2 4 1
    6 6 7

    77. A grassroots group opposed to a proposed increase in the gas tax claimed that the increase would hurt working-class people the most, since they commute the farthest to work. Suppose that the group randomly surveyed 24 individuals and asked them their daily one-way commuting mileage. The results are as follows.

    Working-Class Professional (middles incomes) Professional (wealthy)
    17.8 16.5 8.5
    26.7 17.4 6.3
    49.4 22 4.6
    9.4 7.4 12.6
    65.4 9.4 11
    47.1 2.1 28.6
    19.5 6.4 15.4
    51.2 13.9 9.3

    Determine whether or not the variance in mileage driven is statistically the same among the working class and professional (middle income) groups. Use a 5% significance level.
    81. Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? Suppose that the Table 13.34 shows the results of a study.

    Saturday Sunday Saturday Sunday
    75 44 62 137
    18 58 0 82
    150 61 124 39
    94 19 50 127
    62 99 31 141
    73 60 118 73

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  2. MAR

    STAT 200 Week 7 Homework

    Lane – Ch. 142. The formula for a regression equation is Y’ = 2X + 9.
    a. What would be the predicted score for a person scoring 6 on X?
    b. If someone’s predicted score was 14, what was this person’s score on X?

    6. For the X,Y data below, compute:
    a. r and determine if it is significantly different from zero.
    b. the slope of the regression line and test if it differs significantly from zero.
    c. the 95% confidence interval for the slope.

    X Y
    4 6
    3 7
    5 12
    11 17
    10 9
    14 21

    Lane – Ch. 17
    5. At a school pep rally, a group of sophomore students organized a free raffle for

    prizes. They claim that they put the names of all of the students in the school in

    the basket and that they randomly drew 36 names out of this basket. Of the prize

    winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were
    seniors. The results do not seem that random to you. You think it is a little fishy
    that sophomores organized the raffle and also won the most prizes. Your school is
    composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors.

    a. What are the expected frequencies of winners from each class?
    b. Conduct a significance test to determine whether the winners of the prizes

    were distributed throughout the classes as would be expected based on the

    percentage of students in each group. Report your Chi Square and p values.

    c. What do you conclude?

    14. A geologist collects hand-specimen sized pieces of limestone from a particular

    area. A qualitative assessment of both texture and color is made with the

    following results. Is there evidence of association between color and texture for

    these limestones? Explain your answer.

    Texture Light Medium Dark
    Fine 4 20 8
    Medium 5 23 12
    Coarse 21 23 4

    Illowsky – Ch. 11
    True or False
    70. The standard deviation of the chi-square distribution is twice the mean.
    102. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance.

    French Toast Pancakes Waffles Omelettes
    Men 47 35 28 53
    Women 65 59 55 60

    Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.
    113. df= _______
    117. Let a = 0.05
    Decision: _______
    Conclusion (write out in a complete sentence): _________
    The Regression Equation
    66. Can a coefficient of determination be negative? Why or why not?
    82. The cost of a leading liquid laundry detergent in different
    sizes is given in Table 12.31.

    Size (ounces) Cost ($) Cost per ounce
    16 3.99
    32 4.99
    64 5.99
    100 10.99

    a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.
    b. Does it appear from inspection that there is a relationship between the variables? Why or why not?
    c. Calculate the least-squares line. Put the equation in the form of:ŷ=a+bx
    d. Find the correlation coefficient. Is it significant?
    e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.
    f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.
    g. Does it appear that a line is the best way to fit the data? Why or why not?
    h. Are there any outliers in the given data?
    i. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?
    j. What is the slope of the least-squares (best-fit) line? Interpret the slope

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