THE NUMBER OF GRAMS OF CARBOHYDRATES IN A 12 -OUNCE SERVING OFA REGULAR SOFT DRI

Question

THE NUMBER OF GRAMS OF CARBOHYDRATES IN A 12 -OUNCE SERVING OFA REGULAR SOFT DRINK IS LISTED HERE FOR A RANDOM SAMPLE OF SODAS .ESTIMATE THE MEAN NUMBER OF CARBOHYDRATESIN ALL BRANDS OF SODA WITH95 % CONFIDENCE (ASSUME THE POPULATION IS APROX. NORMAL . 48 37 52 40 43 46 41 38 41 45 45 33 35 52 45 41 30 34 46 40 THE NUMBER OF GRAMS OF CARBOHYDRATES IN A 12 -OUNCE SERVING OFA REGULAR SOFT DRINK IS LISTED HERE FOR A RANDOM SAMPLE OF SODAS .ESTIMATE THE MEAN NUMBER OF CARBOHYDRATESIN ALL BRANDS OF SODA WITH95 % CONFIDENCE (ASSUME THE POPULATION IS APROX. NORMAL . 48 37 52 40 43 46 41 38 41 45 45 33 35 52 45 41 30 34 46 40

Explanation / Answer

sample size, n =20
sample mean, x = 41.6
standard deviation, s = 5.995
standard error, e = s/n =    5.995 /20 = 1.34
degree of freedom , df = n-1 = 20-1=19
at 95% confidence, i.e =0.05, df = 19 and twotail distribution, t = 2.093                                (from t-table) confidence interval = x ± t*e = 41.6 ± (2.093*1.34) = (38.8,44.4) hence at 95% confidence the true mean number of carbohydratesin all brands of soda is between 38.8 and 44.4.

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