Investigation 3:

Please answer D,G, H, I, J, K, L, M

Building a Sampling Distribution (no data set) We will use the Sampling Distribution applet in StatCrunch to investigate properties of the sampling distribution of United States residents over the age of 25 that have obtained a bachelor's degree or higher from the previous investigation. Remember, the given probability of a US resident from having attained a bachelor's degree or higher is 0.3313. We will begin by taking a sample of seven. Under Applets Sampling distributions (box shown below). First, select Binary for the population. Next, to the right of "p:", enter 0.3313. Then click on Compute!

a) Once the applet box is opened, enter 7 in the box to the right of the words "sample size" in the right middle of the applet box window (see image below). Then, at the top of the applet, click "1 time." Watch the resulting animation.

b) Click "Reset" at the top of the applet. Then, click the "1000 times" to take 1000 samples of size 7. Copy and paste the applet image into your solutions.

c) Describe the shape of the Sample Proportions graph at the bottom of your image from part (b) in one sentence.

d) Use the Central Limit Theorem large sample size condition to determine if it is reasonable to approximate this sampling distribution as Normal. Explicitly show these calculations for the condition in the answer. incude a one-sentence explanation on the condition and the calculations.

e) Click Reset at the top of the applet. Enter 77 in the sample size box. Then, click the "1000 times" to take 1000 samples of size 77. Copy and paste the applet image into solutions.

f) Describe the shape of the Sample Proportions graph at the bottom of the image from part (e) in one sentence.

g) Why do you think that this graph from part (e) has the shape described? Use the Central Limit Theorem large sample size condition to answer this question in one sentence. Explicitly show these calculations for the condition in the answer.

h) Using the image in part (e), write the values obtained for the mean (in green) and the standard deviation (in blue). These values are found in the bottom right box labeled "Sample Prop. of 1s."

i) Compare the mean value of the sampling distribution (in green, found in part (h)) to the known population proportion in one sentence in context. Make sure to reference the values in the comparison.

j) Now calculate the standard error of the sample proportion using p = 0.3313 and n = 77 by hand. Record calculations and round answer to four decimal places.

k) Compare the value of the standard error of the sample proportions in part (j) to the standard deviation of the sampling distribution (in blue) obtained in part (h) in one sentence in context. Make sure to reference the values in the comparison.

l) Use the sampling distribution to calculate the probability that from a sample of 77 US residents over the age of 25 that a majority of the US residents in the sample (more than 50%) have attained a bachelor's degree or higher. Record all calculations and the answer in the solutions.

m) Verify the answer in part (l) using the StatCrunch Normal calculator (Stat Calculators Normal) and copy this image in the solutions. Also, in one complete sentence interpret the resulting probability in context of the question. Hint: use the values from part (l) in the calculator.