Question

A company produces chairs. The weekly production follow normal

distribution with mean 200 and standard deviation 0 = 16.
Recently new production methods have been introduced. The
maneger would like to know if there has been a change in the
weekly production A sample of 50 chairs is selected. The sample
mean is 203.5 Test using 0.01 significance level.

Answer 1

The calculated value Z = 1.548 < 2.326 at 0.01 level of significance

The Null Hypothesis is accepted

There is no change in the weekly production

Explanation:

Step(i):-

Given that the mean Population(μ) = 200

Given that the standard deviation of the Population(σ) =16

Given that the mean of the sample (x⁻) = 203.5

Given that the size of the sample(n) = 50

Level of significance = 0.01

Critical value Z₀.₀₁ = 2.326

Null hypothesis : (μ) = 200

Alternative Hypothesis : (μ) ≠200

Step(ii):-

Let 'X' be a random variable in a normal distribution

Test statistic

`Z = (x^(-) -mean)/((S.D)/(√(n) ) )`

`Z = (203.5 -200)/((16)/(√(50) ) )`

Z = 1.548

The calculated value Z = 1.548 < 2.326 at 0.01 level of significance

The Null Hypothesis is accepted

Final answer:-

There is no change in the weekly production