1 0 2 90ofall 005 x values x z1645 99 confidence

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Unformatted text preview: Interval σ 90% .10 .05 x ±16 5 .4 1.645 95% .05 .025 1.960 99% .01 .005 x ±19 0 .6 2.576 x ±25 6 .7 Interval Estimation Sampling distribution of x α/2 1 ­ α of all values x zα / 2 σ x µ α/2 x zα / 2 σ x n σ n σ n 95% Confidence Level Interval Estimation 0 .0 5 /2 =0.025 z = ­1.96 Sampling distribution of x 0 .0 5 /2 95% of all =0.025 x values µ x z = 1.96 90% Confidence Level Interval Estimation 0 .1 0 /2 =0.05 z = ­1.645 Sampling distribution of x 0 .1 0 /2 90% of all =0.05 x values µ x z = 1.645 90% Confidence Level Interval is smaller (i.e., more accurate than for 95%), but we have less confidence (i.e., only 90% confident) Interval Estimation 0 .1 0 /2 =0.05 z = ­1.645 Sampling distribution of x 0 .1 0 /2 90% of all =0.05 x values µ x z = 1.645 99% Confidence Level Interval Estimation 0 .0 1 /2 =0.005 z = ­2.576 Sampling distribution of x 0 .0 1 /2 99% of all =0.005 x values µ x z = 2.576 99% Confidence Level Interval is larger (i.e., less accurate than for 95%), but we have more confidence (i.e., 99% confident) Interval Estimation 0 .0 1 /2 =0.005 z = ­2.576 Sampling distribution of x 0 .0 1 /2 99% of all =0.005 x values µ x z = 2.576 Reducing Margin of Error x ±z 2 α σ n How can the width of a confidence interval be reduced? reduce the population variance increase the sample size reduce the confidence level (1 – α) Interval Estimation Example 1 Interval Estimation A paper manufacturer has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 11 inches, and the standard deviation of the length is 0.02 inches. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal to 11 inches or whether something has gone wrong with the production process to change the length of the paper produced. You select a random sample of 100 sheets, and the mean paper length is 10.998 inches. Construct a 95% and a 99% confidence interval estimate for th...
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