Question

A public health department wants to determine the rate that parents of teen boys are choosing to vaccinate their sons for HPV within the state of Indiana. They conduct a survey of 64 randomly selected families of teen boys.They found that 12% of families had chosen to vaccinate. Which of the following is true?A. The 95% confidence interval is 12% ± the margin of error*standard deviationB. The confidence interval should not be calculated due to the small sample sizeC. A 99% confidence interval will be smaller than the 90% confidence intervalD. The central limit theorem applies to proportions only when the population standard deviation is known

Answer 1

The correct option is B

Explanation:

From the question we are told that

The sample size is
`n  =  64`

The proportion that choose to vaccinate the teen boys is
`\r p =  0.12`

considering the first statement

The 95% confidence interval is 12% ± the margin of error*standard deviation is false because

The 95% confidence interval is is %12 ± the margin of error

considering the second statement

The confidence interval should not be calculated due to the small sample size is true because from the central limit theorem

np = 64 * 0.12 = 7.68

and this value is less than 10 hence the confidence interval should not be calculated

considering the third statement

A 99% confidence interval will be smaller than the 90% confidence interval is false

This is because as the confidence level increase (for example from 90% to 99%) the margin of error increase which increases the confidence interval