A recent study of 5 employees of XYZ company showed that the mean of the distance they traveled to work was 13.2 miles. The standard deviation of the sample mean was 2 miles.distance12.513.211.814.413.9Find the best point estimate of the true mean. Find the 90% upper confidence interval of the true mean.
Question
A recent study of 5 employees of XYZ company showed that the mean of the distance they traveled to work was 13.2 miles. The standard deviation of the sample mean was 2 miles.distance12.513.211.814.413.9Find the best point estimate of the true mean. Find the 90% upper confidence interval of the true mean.
Solution
The best point estimate of the true mean is the sample mean itself. In this case, it is 13.2 miles.
To find the 90% upper confidence interval of the true mean, we first need to find the standard error of the mean (SEM). The SEM is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard deviation is 2 miles and the sample size is 5.
SEM = 2 / sqrt(5) = 0.8944 miles
Next, we need to find the z-score that corresponds to a 90% confidence level. The z-score for a 90% confidence level is 1.645 (you can find this value in a standard z-table or use a calculator).
The margin of error (ME) is then calculated by multiplying the SEM by the z-score.
ME = 1.645 * 0.8944 = 1.47 miles
Finally, the upper confidence interval is calculated by adding the ME to the sample mean.
Upper confidence interval = 13.2 + 1.47 = 14.67 miles
So, the 90% upper confidence interval of the true mean is 14.67 miles.
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