Question

People were polled on how many books they read the previous year. Initial survey results indicate that s=13.5 books.

a. How many subjects are needed to estimate the mean number of books read the previous year within four books with 95% confidence?

b. How many subjects are needed to estimate the mean number of books read the previous year within two books with 95% confidence?

c. What effects does doubling the required accuracy have on the sample size?

1. Doubling the required accuracy nearly quarters the sample size

2. Doubling the required accuracy nearly doubles the sample size

3. Doubling the required accuracy nearly quadruples the sample size.

4. Doubling the required accuracy nearly halves the sample size

d. How many subjects are needed to estimate the mean number of books read the previous year within four books with 99% confidence?

Answer 1

(A) We know the formula for sample size is given as

where , ME(margin of error)= 4 and z = 1.96 for 95% confidence interval (using z distribution table)

setting the given values, we get

Rounding it off to next whole number, we get sample size n = 44 books

(B) We know the formula for sample size is given as

where , ME(margin of error)= 2 and z = 1.96 for 95% confidence interval (using z distribution table)

setting the given values, we get

Rounding it off to next whole number, we get sample size n = 176 books

(C) It is clear from the calculation in part A and B, that when the accuracy is doubled, the sample size increased from 44 to 176

i.e. 176/44 = 4 times

So, sample size is increased 4 times

option C is correct

(D) We know the formula for sample size is given as

where , ME(margin of error)= 4 and z = 2.58 for 95% confidence interval (using z distribution table)

setting the given values, we get

Rounding it off to next whole number, we get sample size n = 76 books