Question

Question: For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p.

a. n = 400,$\hat{p}$= .10

b. n = 50,$\hat{p}$= .10

c. n = 20,$\hat{p}$= .5

d. n = 20,$\hat{p}$= .3

Short answer

Answer

1. Large
2. Not large
3. Not large
4. Not large

Step-by-step solution

Determining whether the sample size is large when n is 400 and p⏞ is 0.10

$a.Theproductofnand\overbrace{p}andtheproductofnand(1-)isshownbelow:$

As both the values are above 15, the sample size is quite large.

Determining whether the sample size is large when n is 50 and p⏜is 0.10

The product of n and $\overbrace{p}$and the product of n and (1-$\overbrace{p}$)is shown below:

As one of the values is not above 15, the sample size is not large.

Determining whether the sample size is large when n is 20 and p^ is 0.5

c.

The product of n and and the product of n and (1-) is shown below:

As both the values are not above 15, the sample size is not large.

Determining whether the sample size is large when n is 20 and p⏞ is 0.3

d.

The product of n and $\overbrace{p}$and the product of n and (1-width="11">p⏜) is shown below:

As both the values are not above 15, the sample size is not large.