Question

6.2.20-T Question Help In a random sample of four mobile devices, the mean repair cost was $90.00 and the standard deviation was $13.00. Assume the population is normally distributed and use a t-distribution to find the margin of error and construct a 90% confidence interval for the population mean. Interpret the results.

Answer 1

solution:-

mean = 90 , standard deviation = 13 , n = 4

degree of freedom df = n - 1 = 4 - 1 = 3

we look into t-distribution table with df and with 90% confidence level

critical value t = 2.353

confidence interval formula

=> mean +/- margin of error

=> mean +/- t * standard deviation/sqrt(n)

=> 90 +/- 2.353 * 13/sqrt(4)

=> 90 +/- 15.29

=> (74.71 , 105.29)

the 90% confidence interval for the population mean is (74.71 , 105.29)

the margin of error is 15.29

=> interpret the result

With 95% confidence, it can be said that the population mean repair cost is between the bounds of the confidence interval.