Question

In a random sample of six mobile devices, the mean repair cost was $70.00 and the standard deviation was $11.00. Assume the population is normally distributed and use a t-distribution to find the margin of error and construct a 95% confidence interval forte population mean. Interpret the results. The 95% confidence interval for the population m ean μ is (DO). Round to two decimal places as needed.) The margin of error is s (Round to two decimal places as needed.) Interpret the results. Choose the correct answer below. O A. With e5% confidence, it can be said that the repair cost is between the bounds of the confidence interval. O B. lt can be said that 95% of mobile devices have a repair cost between the bounds ofthe confidence interval. O c. If a large sample of mobile devices are taken approximately 95% of them will have repair costs between te bounds of the confidence interval. O D. With 95% confidence, it can be said that the population mean repair cost is between the bounds of the confidence interval.

Answer 1

Answer

we have

degree of freedom = n-1 = 6-1 = 5

using t distribution table with degree of freedom 5 and significance level of 0.05, we get

t critical = 2.57

(A) formula for the confidence interval is given as

setting the given values, we get

this gives us

Required confidence interval is (58.46,81.54) (rounded to two decimals)

(b) Margin of error =

setting the given values, we get

margin of error = (rounded to two decimals)

We calculate confidence interval for the population mean, So option D is correct regarding the interpretation of confidence interval.