Question

In a random sample of twelve cell​ phones, the mean full retail price was ​$496.50 and the standard deviation was ​$187.00. Assume the population is normally distributed and use the​ t-distribution to find the margin of error and construct a 90% confidence interval for the population mean μ. Interpret the results. Identify the margin of error. ? dollars cell phones square dollars ​(Round to one decimal place as​ needed.)

Answer 1

Solution:-

Let X: Retail price of cellphone

We have random sample of n=12 cellphone having

Sample mean= = $ 496.50

Sample Standard deviation = ​​​​​= $ 187.00

The confidence interval for mean is

Where,

And

Here,

And

n-1 = 12-1 = 11

Therefore,

Therefore

Now,

90% confidence interval for population Mean is

Result:-(rounded to 1 decimal places)

1)Margin of error = $ 96.9

2) 90% confidence interval for population Mean is

($ 399.6 , $ 593.4)

3) interpretation:-

There is 90% chance that the true population mean belongs to interval ($ 399.6 , $ 593.4)