Mimi is interested in testing the claim that more than 75% of the adults believe
ID: 3131160 • Letter: M
Question
Mimi is interested in testing the claim that more than 75% of the adults believe in global warming. She conducted a survey on a random sample of 100 adults. The survey showed that 80 adults in the sample believe in global warming.
Assume Mimi wants to use a 0.05 significance level to test the claim.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that more than 75% of the adults believe in global warming? Explain.
Explanation / Answer
Set Up Hypothesis
Null, H0:P<=0.75
Alternate,more than 75% of the adults believe in global warming H1: P>0.75
Test Statistic
No. Of Success chances Observed (x)=80
Number of objects in a sample provided(n)=100
No. Of Success Rate ( P )= x/n = 0.8
Success Probability ( Po )=0.75
Failure Probability ( Qo) = 0.25
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.8-0.75/(Sqrt(0.1875)/100)
Zo =1.1547
| Zo | =1.1547
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.155 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 1.1547 ) = 0.12411
Hence Value of P0.05 < 0.12411,Here We Do not Reject Ho
We don't have evidence that more than 75% of the adults believe in global warming