A 2008 Gallup poll showed that 58 of the general public thou

A 2008 Gallup poll showed that 58% of the general public thought human activities impacted global temperature.

If the entire sample was 2,000 people, did more than 50% of the general public think that human activities impacted global temperature? List the null hypothesis, alternative hypothesis, and p-value for this test.

For the test in part a, what is the rejection region for an of 1%?

For the test in part a, with an of 1%, what is , the probability of a type II error?

Solution

Set Up Hypothesis
Null, H0:P=0.5
Alternate, H1: P>0.5
Test Statistic
No. Of Success chances Observed (x)=1160
Number of objects in a sample provided(n)=2000
No. Of Success Rate ( P )= x/n = 0.58
Success Probability ( Po )=0.5
Failure Probability ( Qo) = 0.5
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.58-0.5/(Sqrt(0.25)/2000)
Zo =7.1554
| Zo | =7.1554
Critical Value
The Value of |Z | at LOS 0.01% is 2.33
We got |Zo| =7.155 & | Z | =2.33
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 7.15542 ) = 0
Hence Value of P0.01 > 0,Here we Reject Ho

more than 50% of the general public think that human activities impacted global temperature