Question

U.S. schools face an ongoing challenge: as students get closer to high school graduation, their enthusiasm for school falls. A Gallup poll in June 2017 has discovered that fifth graders are most engaged with school, while 11^th graders are least. The latest Gallup poll showed that only 32% of 11^th graders are engaged in school. Assume this value represents the population proportion. Suppose we randomly sample 150 11^th graders in the U.S. and ask them their engagement in school. ?

A). If samples of size 150 are taken, find the mean, µ?, and standard error, ??, of the resulting sampling distribution of sample proportions, ?.

B). What does this sampling distribution represent?

C). Based on the mean and standard error, label the values of a through g on the normal distribution below. The values are one standard deviation apart.

D). Use the empirical rule to find the interval centered at p that contains approximately 99.7% of all sample proportions.

E). What sample proportions would you consider unusual? Given two examples, one on each side of the mean.

F). In a random sample of 150 11^th graders in the U.S., only 24.7% say they are engaged in school.

            (i) Find the Z-score for this sample proportion. Is this sample proportion unusual?

            (ii) Using technology to find the probability that in a random sample of 150 11^th graders, 24.7% or less will say they are engaged in school.

G). In another random sample of 150 11^th graders, 68 say they are engaged with their school work.

            (i) Find the sample proportion, ?, and find the Z-score for this sample proportion. Is this sample proportion unusual?

            (ii) Find the probability that, among a random sample of 150 11^th graders, 68 or more will say global warming is a serious threat.

Answer 1

0:31 0-150 20 25 sdm

Camlin Page DateI 0 038 0.321 0.038 ) C-281 0.32 1 0.1143 ( O. 2057ーテー0.4343 245g 0.3462) Ps0.3 ax usual

Zsco 247-0. 2.2 0:0 33) 10 CpL0 241 .0277 sam Tr 20 LL-2-204533-0.32 ! 0.038, 0.000 2 30