Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 412 gram setting. It is believed that the machine is underfilling the bags. A 28 bag sample had a mean of 404 grams with a standard deviation of 29. Assume the population is normally distributed. A level of significance of 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:

Claim : < 412

So , the null and alternative hypothesis are

H₀: =  412 vs H₁: < 412

The test statistics t is given by ..

t =  

= (404 - 412)/(29/28)

= -1.460

Now , obsrve H1. < sign indicates that , Left tailed test(one tailed left sided)

df = n - 1 = 28 - 1 = 27

Use t table , see 27 df. See where the value 1.460 fits at one tail alpha value.

0.05 < p value < 0.10

(0.05 , 0.10)

p value = 0.0779