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In: Statistics and Probability

6.14 Changing the confidence level. Consider the settings of the previous two exercises. Suppose that the...

6.14 Changing the confidence level. Consider the settings of the previous two exercises. Suppose that the sample mean is still 78, the sample size is 64, and the population standard deviation is 20. Make a diagram similar to figure 6.6 page 353 (9th edition intro to practice of statistics Mccabe/Moore/Craig) that illustrates the effects of the confidence level on the width of the interval. Use 80%, 90%, 95% and 99%. Summarize what the diagram shows.

Expert Solution

The confidence interval for the population mean (population standard deviation is known) is computed using the formula,

Where,

80% Confidence Interval

The critical value for the significance level = 0.20 is obtained from z distribution table,

90% Confidence Interval

The critical value for the significance level = 0.10 is,

95% Confidence Interval

The critical value for the significance level = 0.05 is,

99% Confidence Interval

The critical value for the significance level = 0.01 is,

From the diagram we can see that as the confidence interval increases margin of error increases such that we are more confidence that the value will lie in that interval.

orchestra answered 1 year ago

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