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24 December, 04:23

A dieter believes that the average number of calories in a homemade peanut better cookie is more than the average number of calories in a store-bought peanut better cookie. which excel statements will estimate the difference in mean calories between the two types of cookies using a 90% confidence interval. the data are: homemade store-bought sample size 40 45 mean number of calories 180 179 standard deviation 2 4

a. = (180-179) + (1.96) (0.6749), and = (180-179) - (1.96) (0.6749)

b. = (180-179) + (1.645) (0.6749), and = (180-179) - (1.645) (0.6749)

c. = (45-40) + (1.96) (0.6749), and = (45-40) - (1.96) (0.6749)

d. = (45-40) + (1.645) (0.6749), and = (45-40) - (1.645) (0.6749)

e. none of the above.

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Answers (1)
  1. 24 December, 04:40
    0
    The confidence interval formula is computed by:

    Xbar ± Z s / sqrt (n)

    Where:

    Xbar is the mean

    Z is the z value

    S is the standard deviation

    N is the number of samples

    So our given are:

    90% confidence interval with a z value of 1.645

    Sample size 40, 45

    Mean 180, 179

    Standard deviation 2, 4

    So plugging that information in the data will give us a confidence interval:

    For 1:

    Xbar ± Z s / sqrt (n)

    = 180 ± 1.645 (2 / sqrt (40))

    = 180 ± 1.645 (0.316227766)

    = 180 ± 0.520194675

    = 179.48, 180.52

    For 2:

    Xbar ± Z s / sqrt (n)

    = 179 ± 1.645 (4 / sqrt (45))

    = 179 ± 1.645 (0.596284794)

    therefore, the answer is letter b
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