Question

Gallup reported in March 2012 that 73% of American investors say that a politically divided federal government investors say that a politically divided federal government is hurting the u.s investment climate “ a lot “ is there any evidence that the percentage has changed significantly from the 74% reported in September 2011? ( these results are based on questions asked of a random sample of 1022 U.S adults investable assets of 10,000 or more)

a) find the z-score of the observed proportion

b) is there evidence that the proportion has decreased?

c) explain your conclusion

Please show work

Answer 1

Solution:

Given: Gallup reported in March 2012 that 73% of American investors say that a politically divided federal government investors say that a politically divided federal government is hurting the u.s investment climate “ a lot “.

We have to test if there is any evidence that the percentage has changed significantly from the 74% reported in September 2011.

Thus Sample proportion = and Population proportion = p = 0.74

Sample size = n = 1022

Part a) Find the z-score of the observed proportion

Part b) is there evidence that the proportion has decreased?

Thus hypothesis would be:

H0: p = 0.74 Vs H1: p < 0.74

and critical value at 0.05 level of significance is:

look in z table for Area = 0.0500 or its closest area and find z value

Area 0.0500 is in between 0.0495 and 0.0505 and both the area are at same distance from 0.0500

Thus we look for both area and find both z values

Thus Area 0.0495 corresponds to -1.65 and 0.0505 corresponds to -1.64

Thus average of both z values is : ( -1.64+ - 1.65) / 2 = -1.645

Thus Z = -1.645

Decision rule: Reject H0, if z test statistic value < z critical value = -1.645, otherwise we fail to reject H0.

Since z test statistic value = z = -0.73 is not less than z critical value = -1.645, we fail to reject H0.

Thus there is no evidence that the proportion has decreased.

Part c) explain your conclusion

Since there is no evidence that the proportion has decreased as well as z score is within 2 standard deviation , thus there is no  evidence that the percentage of American investors say that a politically divided federal government investors say that a politically divided federal government is hurting the u.s investment climate “ a lot “ has changed significantly from the 74% reported in September 2011.