Question

A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 16 ounces. The distribution of weight is known to be normal, with a standard deviation of 0.4 ounce. A random sample of 16 boxes yielded a sample mean weight of 15.84 ounces calculate the P-value of the test

Answer 1

To calculate the P-value we need to calculate T-statistics first

$t = (x-μ) / (s/√n)$  

where x is the sample mean, μ is the hypothesized mean, s is the sample standard deviation, and n is the sample size

then

$t= - 1,6$

Using the t-distribution table we state that the our t-value corresponds the p-value of 0,05

Answer $p = 0,05$