Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the adults who think that the U.S. government is doing too little to protect the environment presently and the adults who think that the U.S. government is doing too little to protect the environment 10 years ago. The population proportions would be p1 and p2 respectively.
p1 - p2 = difference in the proportion of adults who think that the U.S. government is doing too little to protect the environment presently and the adults who think that the U.S. government is doing too little to protect the environment 10 years ago.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 ≠ p2
p1 - p2 ≠ 0
it is a two tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples
For the present,
x1 = 580
n1 = 1066
p1 = 580/1066 = 0.54
For 10 years ago,
x2 = 514
n2 = 1038
P2 = 514/1038 = 0.5
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (580 + 514)/(1066 + 1038) = 0.52
1 - pc = 1 - 0.52 = 0.48
z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.54 - 0.5)/√(0.52)(0.48)(1/1066 + 1/1038) = 0.04/0.02178551744
z = 1.84
Since it is a two tailed test, the curve is symmetrical. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the test z score in the right tail 1 - 0.967 = 0.033
We would double this area to include the area in the left tail of z = - 1.84 Thus
p = 0.033 × 2 = 0.066
Alpha = 0.1
Since alpha, 0.1 > p value 0.066, we would reject the null hypothesis.
Therefore, at a = 0.10, we can reject the
claim that the proportion of U.S. adults who think that the U.S. government
is doing too little to protect the environment has not changed.
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