Question

. A machine is expected to produce nails of length 3 cm. A random sample of 25 nails gave an average length of 3.1 cm with SD 0.3 cm. can it be said that the machine is producing nails as per specification. (Given value of toos for 24 df is 2.064)
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Answer 1

Answer:

Step 1:

Null Hypothesis (H0):μ=5(H0):μ=5 [i.e The performance of machine to justify the claim]

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

Step 2:

Let LOS= 5%5% [two tailed test]

critical value (zx)=1.96(zx)=1.96

Step 3:

Since sample is large

S.E=σn−−√=0.45100−−−√=0.045S.E=σn=0.45100=0.045

Step 4: Test statistic

Zcal=x−−−μS.E=5.1−50.045=2.2222Zcal=x_−μS.E=5.1−50.045=2.2222

Step 5: Decision

Since Zcal>zx,H0Zcal>zx,H0 is rejected

The performance of the machine does not justify the claim.