Question

In November 2009, 65% of Americans
favored the death penalty for the crime
of murder. Just a few months ago,
Monmouth University ran another poll of
1025 Americans and found 653
Americans favored the death penalty in
murder cases.

1. Does the new poll indicate that American
opinion on the death penalty in murder
cases has changed?

The table below gives the temperatures
at noon at the Nut Tree on a sample of
days last summer.
75. 90
77. 93
84. 93
84. 94
85 101

Answer 1

As we are testing here whether the proportion of Americans who favors the death penalty has changed, therefore this is a two tailed test for which the null and the alternative hypothesis here are given as:

The sample proportion here is computed as:
p = x/n = 653/1025 = 0.6371

The test statistic here is computed as:

As this is a two tailed test, the p-value here is computed as:
p = 2P( Z < -0.87)

Getting it from the standard normal tables, we have here:
p = 2P( Z < -0.87) = 2*0.1922 = 0.3844

As the p-value here is 0.3844 > > 0.1, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence to support the claim that the proportion of Americans who favored the death penalty in
murder cases