Problem done in excel 1.Your principal product is sold in 50 kg bags. The Data (

Question

Problem done in excel

1.Your principal product is sold in 50 kg bags. The Data (after the question), provides 50 random samples from one day’s production.

a.What is a 95% confidence interval for the mean of this sample?

b.If you wanted to measure to within 0.25 (e.g. half-width is 0.25), what sample size would be necessary?

99.7926 100.0007 100.511 98.759 102.0097 100.2975 101.262 100.2236 100.5666 101.4248 99.5152 100.3314 99.9192 98.79106 98.71766 99.54862 101.5318 99.61233 100.4196 100.567 100.4601 101.3936 100.0613 100.9524 99.15766 99.41538 100.6455 99.67488 100.7153 99.99609 101.0688 101.4674 100.682 99.49382 100.1134 100.5169 102.4265 101.2312 99.95577 101.6734 98.88855 99.92572 100.3464 99.79573 99.45857 99.66174 100.7042 100.5978 100.1532 99.99356

Explanation / Answer

a. Here mean=100.2886 and sd=0.8427

t table value is 2.0096

So Margin of error=E=t*sd/sqrt(n)=0.2395

Hence CI=mean+/-E=100.2886+/-0.2395=(100.049,100.528)

b. E=0.25

We know, E=sd*z/sqrt(n)

Hence n=(z*sd/E)^2=(1.96*0.8427/0.25)^2=44

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