Of the population of all fruit flies we wish to give a 90% confidence interval for the fraction which possess a gene which gives immunity to fungal infections. To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene. Give the margin of error for the 90% confidence interval. Round your answer to 3 decimal places.

The margin of error for the 90% confidence interval is of 0.038.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is of:

To this end we have obtained a random sample of 400 fruit flies. We find that 280 of the flies in the sample possess the gene.

This means that

90% confidence level

So , z is the value of Z that has a pvalue of , so .

Margin of error:

The margin of error for the 90% confidence interval is of 0.038.

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