Question

1) If Pete is correct that the population proportion p= 0.30 describe the sampling distribution of sample proportions for simple random samples of n = 150 drawn from the population of college and university students in California.

The words “describe the sampling distribution” mean that you need to specify the shape, center and spread of the sampling distribution. You should also state whether or not the conditions are met for the process you are using and show a calculation to justify that answer.

on your scratch paper show how you calculated the standard deviation and how you assured that the conditions were met.

2)

Calculate the interval of reasonably likely sample proportions if Pete is right, and the population proportion, p = 0.30. In the previous question you should have found that the standard deviation for the sampling distribution of sample proportions is 0.0374. Use these values, do not round until you have finished the computations. Then round to two decimal places.

In your written work show the formula, the values input into the formula, and your final answers. Write your final response as a three part inequality in lower value<correct symbol<upper value.

Answer 1

1) If Pete is correct that the population proportion p= 0.30 describe the sampling distribution of sample proportions for simple random samples of n = 150 drawn from the population of college and university students in California.

We are given:

Population proportion, p= 0.30

Sample size, n = 150

Strandard deviation, σ = √p*(1-p)/n

= √0.30(1-0.30)/150

= 0.0374

The shape of the sampling distribution will be Normal DIstribution.

The center of the sampling distribution will be 0.30.

The spread of the sampling distribution is 0.0374.

All the conditions for the Normal distribution are met.

2) 95% Confidence Interval = p ± z*√p*(1-p)/n

= 0.30 ± 1.96*(√0.30(1-0.30)/150)

= 0.30 ± 0.0733

= (0.30 - 0.0733, 0.30 + 0.0733)

= (0.2267, 0.3733)

Thus, the 95% Confidence Interval is between 0.2267 and 0.3733.