Question

A study is performed to examine the IQ of professional athletes. Of 20 athletes participating in the study, the average IQ is 105 with a standard deviation of 11. Construct a 95% confidence interval for the population mean IQ of professional athletes.

Point Estimate:

Margin of Error: E =

Lower Limit:

Upper Limit:

(Round to four decimal places)

*Please show how to put in TI84 if possible

Answer 1

I don't own a TI84 calculator otherwise would have answered using that. Please find the manually typed solution below:

We need to construct the 95% confidence interval for the population mean μ. The following information is provided:

Sample Mean =	105
Sample Standard Deviation (s) =	11
Sample Size (n) =	20

The point estimate of μ is 105.

The margin of error is

The critical value for α=0.05 and df=n−1=19 degrees of freedom is . The corresponding confidence interval is computed as shown below:

​

Therefore, based on the data provided, the 95% confidence interval for the population mean is 99.8519<μ<110.1481, which indicates that we are 95% confident that the true population mean μ is contained by the interval (99.8519,110.1481)

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