Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 435 gram setting. It is believed that the machine is underfilling the bags. A 6 bag sample had a mean of 425 grams with a standard deviation of 14 . Assume the population is normally distributed. A level of significance of 0.02 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 :

Given that,

Population mean = = 435

Sample mean = = 425

Sample standard deviation = s = 14

Sample size = n = 6

Level of significance = = 0.02

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 435

Ha: 435

The test statistics,

t = ( - )/ (s/)

= ( 425 - 435 ) / ( 14 /6)

= - 1.750

Critical value of  the significance level is α = 0.02, and the critical value for a two-tailed test is

= 3.365

df = n - 1 = 5

P- Value = 0.1406

The p-value is p = 0.1406 > 0.02, it is concluded that the null hypothesis is fails to reject.