Question

to the nearest thousandth, what is the P-Value for a test of the claim that the average new home has at least 1400 square feet, if a random sample of 40 new homes yielded an average of 1235 square feet, with a standard deviation of 152 square feet.

Answer 1

Given that, sample size (n) = 40, sample mean = 1235 square feet and sample standard deviation (s) = 152 square feet

The null and alternative hypotheses are,

H0 : μ ≥ 1400 square feet

Ha : μ < 1400 square feet

This hypothesis test is a left-tailed test.

Test statistic is,

=> Test statistic = -6.865

Degrees of freedom = 40 - 1 = 39

Using Excel we find the p-value,

Excel Command : =TDIST (6.865, 39, 1) = 0.000

=> p-value = 0.000