Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 431 431 gram setting. It is believed that the machine is underfilling the bags. A 23 23 bag sample had a mean of 423 423 grams with a standard deviation of 14 14 . Assume the population is normally distributed. A level of significance of 0.05 0.05 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

Solution:

1)

The null and alternative hypothesis are

H₀ : = 431 vs H₁ : < 431

2)

The test statistic t is

t =   = [423 - 431]/[14/23] = 2.740

3)

df = n - 1 = 23 - 1 = 22

< sign in H₁ indicates that "One tailed Left sided test "

t = 2.740

Using t table ,

0.005 < p value < 0.01

Using calculator ,

p value = 0.0060