A study is to be conducted of the percentage of popcorn seeds that collapse during cooking. How large a sample is required if we wish to be at least 95% confident that the error in estimating this quantity is less than 0.020, regardless of its true value

Using the sample size formula, the number of samples required to obtain the result stated above is 2401.

Given the Parameters :

When the value of the proportion, p isn't given, we take p = 0.5

To obtain the sample size, we use the relation. :

Zcrit = Zcritical at 95% = 1.96 (normal distribution table)

Substituting the values into the relation :

n = 0.5(1 - 0.5)[(1.96 ÷ 0.020)]²

n = 0.25(98²)

n = 0.25(9604)

n = 2401

Therefore, a sample size of 2401 will be required.

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A sample of 2401 is required.

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:

95% confidence level

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

In this question:

We need a sample of n.

n is found when M = 0.02.

We don't know the true proportion, so we use the worst case scenario, which is

A sample of 2401 is required.

x=6 and x=3

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