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Answer :
Final Answer:
The 90% confidence interval for the mean body temperature of adults in the town is (97.993, 98.976)°F. This range suggests that we are 90% confident that the true population mean body temperature falls within this interval, based on the sample data collected. It provides a level of certainty about the accuracy of the estimated population mean from the sample.
a) (97.993, 98.976)
Explanation:
To calculate the 90% confidence interval of the mean body temperature, we use the formula:
[tex]\[ \bar{x} \pm Z_{\alpha/2} \times \frac{s}{\sqrt{n}} \][/tex]
where [tex]\( \bar{x} \)[/tex] is the sample mean,[tex]\( Z_{\alpha/2} \)[/tex] is the critical value from the standard normal distribution corresponding to the desired confidence level (in this case, 90%),[tex]\( s \)[/tex] is the sample standard deviation, and [tex]\( n \)[/tex] is the sample size. From the given data, the sample mean [tex]\( \bar{x} \)[/tex] is 98.279°F, the sample standard deviation [tex]\( s \)[/tex] is 1.042°F, and the sample size [tex]\( n \)[/tex] is 14. The critical value [tex]\( Z_{\alpha/2} \)[/tex] for a 90% confidence interval is approximately 1.645. Substituting these values into the formula, we find the confidence interval to be (97.993, 98.976).
Therefore, the 90% confidence interval of the mean body temperature of adults in the town is (97.993, 98.976)°F. This indicates that we are 90% confident that the true population mean body temperature falls within this interval. It provides a range of values within which we expect the true population mean to lie, based on the sample data collected from the small town.
Option a
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