Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months. A random sample of children will be selected, and the age at which each child begins to walk will be recorded. A 99% confidence interval for the average age at which children begin to walk will be constructed using the data obtained from the sample of children. Of the following, which is the smallest sample size that will result in a margin of error of 0.1 month or less for the confidence interval? a. 400.
b. 900.
c. 1,300.
d. 1,600.
e. 2,100.

d. 1,600.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

That is z with a pvalue of , so Z = 2.575.

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months.

This means that

Of the following, which is the smallest sample size that will result in a margin of error of 0.1 month or less for the confidence interval?

The sample size has to be n or larger. n is found when . So

Multiplying both sides by 10

So the sample size has to be at least 1492, which means that of the possible options, the smallest sample size is 1600, given by option d.

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step-by-step explanation: