Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 405 gram setting. It is believed that the machine is underfilling the bags. A 22 bag sample had a mean of 396 grams with a variance of 441. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal.

Required:
State the null and alternative hypotheses.

Answer 1

We reject H₀

Explanation:

Normal Distribution with n = 22 ( sample size)

n<30 we need to use a t-student distribution

Sample mean μ = 396

Population mean ( required mean ) μ₀ = 405

Sample variance is 441 then sample standard deviation s = √441

s = 21

Hypothesis Test

Null Hypothesis H₀ μ = μ₀

Alternative Hypothesis Hₐ μ < μ₀

Significance level α = 0,1

The test is a one-tail test to the left

From t-student table we find for t(c)

degree of fredom df = 22 -1 df = 21

and α = 0,1 t(c) = - 1,3232

To compute t(s)

t(s) = ( μ - μ₀ ) / s /√n

t(s) = ( 396 - 405 )*√n / 21

t(s) = - 9 *4,69 /21

t(s) = - 2,01

Comparing

t(s) and t(c) - 2,01 and - 1,3232

|t(s)| > |t(c)| then t(s) is in the rejection region we must reject H₀