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Answer :
A. The 90% confidence interval for the population mean is (162.91,167.09)
B. The value Margin of error is 7.42
C. The interpretation of the confidence level obtain from (a) is there is a 90% chance that the interval (162.91,167.09) contains the true population mean.
How can we determine the values given above?
a) A 90% confidence interval for the population mean can be constructed using the following formula:
(sample mean) ± (critical value) x (standard deviation of the mean)
The critical value is determined by the level of confidence and the sample size. For a 90% confidence level and a sample size of 20, the critical value is 1.645.
Therefore, the 90% confidence interval for the population mean is:
165 ± (1.645 x 4.5)
which is (162.91,167.09)
b) The margin of error is the critical value x the standard deviation of the mean, or 1.645 x 4.5 = 7.42.
c) A 90% confidence interval means that if we were to repeat this process many times, 90% of the intervals constructed would contain the true population mean. In other words, there is a 90% chance that the interval (162.91,167.09) contains the true population mean.
Therefore, the correct answer is as given above. It can then be concluded that the values given for 90% confidence interval, margin of error and it's interpretation are as given.
learn more about margin of error: https://brainly.com/question/10218601
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