Question

(a) Use the Excel tab titled SHINGLES to construct 95% confident intervals for the mean pallet weight for each shingle company. (b) In practical terms, interpret both of these confident intervals individually. (c) Compare the two confidence intervals to each other and

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Answer 1

To calculate confidence intervals, we need z-score values for the given confidence

z-values at 0.025 and 0.975 according to the z-table are -1.96 and 1.96

Therefore, the confidence interval can be calculated as (mean+Zlower limit*SD, mean+Z upper limit*SD)

For companies Boston and Vermont, according to the data given, the mean and SD are as follows

Mean_B = 3140 SD_B = 41.36

Mean_V = 3151.7 SD_V = 78.14

Confidence interval for Boston co = (3140-1.96*41.36, 3140+1.96*41.36) = (3058.9, 3221.06)

Confidence interval for Vermont co = (3151.7-1.96*78.14, 3151.7+1.96*78.14) = (2998.54, 3304.85)

b) In practical terms, these intervals can be interpreted as, 95% of the data lies within the interval range. i.e., 95% of the predictions might also fall in this range

c) The confidence interval of Boston co is smaller than that of the Vermont co, to be precise the interval of Boston co is a subset of that of the Vermont co