Question

Asked Dec 15, 2019

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A machine puts out 16 imperfect articles in a sample of 500. After the machine is overhauled it puts 3 imperfect articles in a batch of 100. Has the machine been improved? Use 5% level of significance. Use p-value fot your conclusion and also find 88% confidence interval for difference between population proportion.

Step 1

From the given information, the claim of the problem is the machine has been improved.

** **

**Null Hypothesis:**

*H*_{0}:*p*_{1}=*p*_{2}

**Alternative Hypothesis:**

*H*_{a}:*p*_{1}-*p*_{2}<0

**Test Statistic:**

From the given information, *n*_{1}=500, *x*_{1}=16, *n*_{2}=100 and *x*_{2}=3.

The pooled sample proportion is,

Step 2

The test statistic is ** 0.104** and it is calculated below:

Step 3

*p***-value:**

The *p*-value is **0.5414** and it is calculated below:

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