The sodium content of thirty 300-gram boxes of organic corn flakes was determine

Question

The sodium content of thirty 300-gram boxes of organic corn flakes was determined. The data (in milligrams) are as follows:

131.09 130.02 130.91 129.54 129.64 128.77 130.72 128.33 128.24 129.65 130.14 129.29 128.71 129.00 129.39 130.43 129.53 130.12 129.78 130.92 131.15 130.69 130.91 129.54 129.64 128.77 130.72 128.33 128.24 129.65

Use a = 0.05. Round all intermediate calculations to four decimal places (e.g. 12.3456) and round the final answer to two decimal places (e.g. 98.76).

(a) s =

(b) Can you support the claim that the mean sodium content of this brand of corn flakes is 130 milligrams?

Determine the test statistic t0.

(c) Compute the power of the test if the true mean sodium content is 130.5 milligrams.

Please show work.

Explanation / Answer

a. Here n is 30, mean is 129.73, s is 0.911

s=sqrt(sum(x-mean)2/(n-1)) where mean is sum of value of x/total number.

b. Here n is 30 so we will use t test statistics

Here H0: mu=130

And H1:mu not equal to 130

Test statistics is t=(mean-mu)/(s/sqrt(n))

=>t=129.73-130/0.911/sqrt(30)=-1.62

Now p value is 0.116

Since pvalue > 0.05, we do not reject H0.

c. I have used calculator to compute power and answer is 0.91 source http://www.stat.ubc.ca/~rollin/stats/ssize/n2.html

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