Consider a production process that produces batteries. A quality engineer has taken 20 samples each containing 100 batteries. The total number of defective batteries observed over the 20 samples is 200.

Construct a 95% confidence interval of the proportion of defectives.

Another sample of 100 was taken and 15 defectives batteries were found. What is your conclusion?

The 95% confidence interval for the true proportion of defective batteries is (0.0966, 0.1034).

It is better to take a larger sample to derive conclusion about the true parameter value.

Step-by-step explanation:

The (1 - α) % confidence interval for proportion is:

Given:

n = 2000

X = 200

The sample proportion is:

The critical value of z for 95% confidence interval is:

Compute the 95% confidence interval as follows:

Thus, the 95% confidence interval for the true proportion of defective batteries is (0.0966, 0.1034).

Now if in a sample of 100 batteries there are 15 defectives, the the 95% confidence interval for this sample is:

It can be observed that as the sample size was decreased the width of the confidence interval was increased.

Thus, it can be concluded that it is better to take a larger sample to derive conclusion about the true parameter value.

i would be 2,000 just get the square root of 50 which is 2500 and the divid 4/5 and last thing multiply the answer you get for that by the square root of 50

step-by-step explanation:

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