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    Tootsie Rolls & Pre-employment Drug Tests

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    Please complete the following and note that methods of computation could include the usage of Excel.
    1. A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were

    3.087
    3.131
    3.241
    3.241
    3.270
    3.353
    3.400
    3.411
    3.437
    3.477

    (a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. (Data are from a project by MBA student Henry Scussel.) Tootsie

    2. In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p? (Data are from Flying 120, no. 11 [November 1993], p. 31.)

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    Solution Preview

    Please find the solution in the attached file.

    Solution-1

    (a) Sample mean = ( 3.087 + 3.131 + 3.241+ 3.241+ 3.270 + 3.353 + 3.400 + 3.411 + 3.437
    + 3.477)/10 = 3.3048
    Standard deviation = 0.132

    Confidence Interval =
    ...

    Solution Summary

    Confidence intervals are constructed, sample sizes chosen and factors discussed in these statistic questions.

    $2.19

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