Question

1. 4. A random sample of 8 houses in Scranton yields an average size of 1,966 square feet. The standard deviation for the size of all houses in Scranton is found to be 355 square feet. Assuming that the sizes of all houses in the city have an approximately normal distribution, find a 95% confidence interval for the average size of all houses in Scranton.

Conclusion: We can be __________confident that the mean size of all houses in Scranton is between _____________ and _____________ square feet

Answer 1

mean = 1966 , sigam = 355 , n = 8

The t value at 95% confidence interval is,

alpha = 1 - 0.95 = 0.05
alpha/2 = 0.05/2 = 0.025
t(alpha/2,df) = t(0.025,7) = 2.365

Margin of error = E =z *(s/sqrt(n))
= 2.365 *(355/sqrt(8))
=296.8346

The 95% confidence interval is

mean -E < mu < mean +E

1966 - 296.8346< mu < 1966 +296.8346

1669.1654 < mu < 2262.8346

We can be 95% confident that the mean size of all houses in Scranton is between 1669.1654 and 2262.8346 square feet