Question

a youth director for a city's parks and recreations department is planning for next year's program. From a survey of city residents, the director knows that 35% of the population participate in the parks and recreations programs. For a random sample of 40 people, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?

Answer 1

Solution:

Standard deviation for the sampling distribution of sample proportions is given as follows:

Where, P is population proportion, Q = 1 - P and n is sample size.

Population proportion of people who participate in the parks and recreations programs is, P = 35% = 0.35

Q = 1 - 0.35 = 0.65

Sample size (n) = 40

Hence, standard deviation for the sampling distribution of the sample proportions is given by,

The standard deviation for the sampling distribution of the sample proportions is 0.075.

Please rate the answer. Thank you.