Question

Instructions

The expectation is that you will show how the answers were found and what they mean.

From a survey that Alika conducted for her veterinary medicine class, she found that 365 households out of a total of 1000 households claimed to own at least one dog or cat. Alika constructed a 95% confidence interval in order to predict the population proportion, π, leading to 0.3352 ≤ π≤ 0.3948. (She used the Excel function CONFIDENCE.NORM.)

Alika concluded that:

1) It was Ok to use the sample proportion p = 365/1000 = 0.365 to construct this confidence interval;

2) The proportion of households in her whole state that would claim to own a dog or cat would be between 33.52% and 39.48%; and

3) She was glad that she had not chosen a larger sample because a sample greater than n = 1000 would have caused the confidence interval to become wider and less precise.

Answer 1

Sample proportion p = 365 / 1000 = 0.365

a)

95% confidence interval for is

p - Z/2 * sqrt ( p ( 1 - p) / n) <= <= p + Z/2 * sqrt ( p ( 1 - p) / n)

0.365 - 1.96 * sqrt( 0.365 * 0.635 / 1000) <= <= 0.365 + 1.96 * sqrt( 0.365 * 0.635 / 1000)

0.3352 <= <= 0.3948

b)

We conclude that,

We are 95% confident that population proportion is between 33.52% and 39.48%.

That is,

The proportion of houshold in her whole state that would claim to own a dog or cat would be

between 32.52% and 39.48%