Problems on Confidence Intervals using ta HINTS: Please use the confidence inter

Question

Problems on Confidence Intervals using ta HINTS: Please use the confidence interval formula from the notes. Since we are dealing with problems where the standard deviation sigma is unknown, we will use the t distribution. Instead of looking up z, in the last row of the t table, we look up t in the row for (n-1) degrees of freedom. (n will be specified in the problem) For the problems in which they ask you to find the minimum sample size, you will be solving for n. You have to take E, the Margin of sampling error (specified in the problem) and set it equal to the E formula, which is: E s(za from last row of t table (sigmay(radical n) and solve for n. (Always use z for this, and not t, since t is based on (n-1), and n is what you are looking for in these kinds of problems.) round up to the next integer if your answer is not integer valued The length of the confidence interval is 2 times the error E. (L 2 E) This is because in creating a confidence interval, you start at X-bar and move a distance of E to the right, and a distance of E to the left, thus, Le 2E.

Explanation / Answer

here

a) Xbar =86.2

b) s =11.745

c)degree of freedom =n-1=10-1=9

d)for 90% CI, t=1.833

hence confidence interval =sample mean -/+ t*std error =84.367 ; 88.033

e)for length =UCL-lCL =88.033-84.367 =3.666

X 82.000 66.000 90.000 84.000 75.000 88.000 82.000 94.000 110.000 91.000 mean(X) 86.200 std deviation(S) 11.745 std error =S/(n)1/2 3.714

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