Question

A random sample of 68 households was selected for a phone survey. The key question asked​ was, "Do you or any member of your household own a product from Company​ A?" Of the 68 ​respondents, 34 said yes and 34 said no. a. Determine the sample​ proportion, p, of households that own a Company A product. b. If the population proportion is 0.75​, determine the standard error of the proportion.

Answer 1

a. p = 0.5

b. SE = 0.0525

Explanation:

a. The sample proportion (p) of households that own a Company A product is given by the number of people who answered "yes"(34) divided by the sample size (n=68)

`p = (34)/(68)=0.5`

The sample proportion is 0.5.

b. If the population proportion is P = 0.75, the standard error is given by:

`SE=\sqrt{(P*(1-P))/(n)}\\SE=\sqrt{(0.75*(1-0.75))/(68)}\\ SE=0.0525`

The standard error is 0.0525.