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    Sampling and Hypothesis Testing Questions

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    1. Find the critical value X2 0.99 associated with a X2 curve with 10 degrees of freedom.

    2. Find the critical value having an area of 0.05 to its right for an F-curve with 8 numerator degrees of freedom and 15 denominator degrees of freedom.

    3. A random sample of 100 adults was recently gathered in order to explore a possible relationship between alcohol consumption and high blood pressure. The results are provided in the contingency table below. Your job is to determine if drinking status is independent of high blood pressure.

    a. Define the null and alternative hypotheses associated with the 2 test for
    independence.
    b. Complete the contingency table by finding expected values.
    c. Let = 0.10. Find and sketch the rejection region associated with this
    hypothesis test.
    d. Compute the 2 test statistic and state your conclusion.
    Absent Present Total
    Drinking
    non drinker
    26 11 37
    Status
    light to moderate
    16 29 45
    heavy drinker 13 5 18
    Total 55 45 100
    17

    4. The types of raw material used to construct stone stools found at the archaeological site Casa del Rito are shown below. (Bandelier Archaeological Excavation Project edited by Kohler and Root). A random sample of 1486 stone tools are obtained from a current excavation site.
    a. Test the claim that the regional distribution of raw materials fits the distribution at the current evaluation site. State null and alternative hypothesis.
    b. Let a = 0.10. Find and sketch the rejection region associated with this hypothesis test.
    c. Compute the X2 test statistic and state your conclusion.

    5. The presence of harmful insects in farm fields is detected by erecting boards covered with a sticky substance and then examining the insects trapped on the board. To investigate which colors are most attractive to cereal leaf beetles, researchers placed six boards of each of four colors in a field of oats. The table below gives data on the number of cereal leaf beetles trapped.
    a. Compare the means for the four colors.
    b. Test the hypothesis that the color of the board has no effect in attracting cereal leaf beetles at = 0.05, assuming that the number of insects trapped follows a normal distribution and that the standard deviations are the same for all colors.
    c. Do these assumptions seem reasonable? Why or why not?

    Raw Material
    Regional Percent of Stone Tools
    Observed Number of Tools at Current Excavation Site
    Basalt
    61.30%
    906
    Obsidian
    10.60%
    162
    Welded tuff
    11.40%
    168
    Pedernal chert
    13.10%
    197
    Other
    3.60%
    53
    Total
    100%
    n = 1486
    ColorYellow455948463847White211214171317Green373215253941Blue16112021147Insects Trapped
    18

    6. Manatees are large sea creatures that live in the shallow water along the coast of Florida. Many manatees are injured or killed each year by powerboats. Here are the data on manatees killed and powerboat registration (in thousands of boats) in Florida for the period 1984 to 1990.
    a. Complete the table.
    b. Using the table, find the following values: xx yy xy x, y, S , S , and S .
    c. Using and b y b x

    S
    S
    b
    xx
    xy
    1 0 1 find the regression equation
    y b b x 0 1

    d. What is the coefficient of determination, 2 r ?
    e. If Florida were to limit powerboat registration to a maximum of 700,000 boats (x = 700) how many manatees could we expect to be killed?

    7. Applicants for a particular job that involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish. The sample data below was obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.
    Partial Minitab output is provided below.
    Mintab -- Regression Analysis
    The regression equation is score = 31.5 + 10.9*years
    S = 5.651 R-Sq = 83.0% R-Sq(adj) = 80.9%
    Analysis of Variance
    Source DF SS MS F P
    Regression 1 1248.6 1248.6 39.09 0.000
    Residual Error 8 255.5 31.9
    Total 9 1504.1
    Powerboats Manatees
    registration killed
    1984 559 34 312481 1156 19006
    1985 585 33 342225
    1986 614 33 1089 20262
    1987 645 39 416025 1521
    1988 675 43 29025
    1989 711 50 505521 2500 35550
    1990 719 47 2209
    SUMS 4508 2925834 182096
    Year
    2 x 2 y xy x y
    Number of Years (x ) 3 4 4 2 5 3 4 5 3 2
    Score (y ) 57 78 72 58 89 63 73 84 75 48

    a. What is the correlation coefficient, r?
    b. At the 5% level of significance, do the data provide sufficient evidence to conclude that the slope of the population regression line is not zero and hence that the number of years of study is useful as a predictor of score on the test?
    c. Do the data provide sufficient evidence to conclude that the number of years of study and test score are linearly positively correlated? Use = 0.01.

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