Does the performance of the machine justify the claim? Mention the level of significance you apply

Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 05

Year : DEC 2014

$n = 100$ [ \gt 30; so it is a large sample] $$\underline x= 5.1, σ= 0.45$$

Step 1:

Null Hypothesis $(H_0): μ= 5$ [i.e The performance of machine to justify the claim]

Alternative Hypothesis $(H_a): μ≠5$ [i.e The performance of machine does not justify tha claim] (Two tailed test)

Step 2:

Let LOS= $5\%$ [two tailed test]

critical value $(z_x) = 1.96$

Step 3:

Since sample is large

$S.E = \dfrac σ{\sqrt n}= \dfrac {0.45}{\sqrt{100}}= 0.045$

Step 4: Test statistic

$Z_{cal} = \dfrac {\underline x-μ}{S.E}= \dfrac {5.1-5}{0.045}= 2.2222$

Step 5: Decision

Since $Z_{cal} \gt zx , H_0$ is rejected

The performance of the machine does not justify the claim.