Question

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly different from 66% at a significance level of αα = 0.10. According to your sample, 60 out of 96 potential voters prefer Candidate A.

1. For this study, we should use Select an answerχ²-Testχ²GOF-Test2-PropZInt2-SampTInt1-PropZInt2-PropZTestANOVA2-SampTTestT-TestTInterval1-PropZTest
2. 
   
3. The null and alternative hypotheses would be:   
     H0H0: ?μp ?≠><= (please enter a decimal)   
     H1H1: ?μp ?<=>≠ (Please enter a decimal)   
4. 
   
5. The test statistic = (please show your answer to 3 decimal places.)
6. 
   
7. The p-value = (Please show your answer to 4 decimal places.)
8. 
   
9. The p-value is Select an answergreater thanless than (or equal to) αα
10. 
    
11. Based on this, we should Select an answerrejectacceptfail to reject the null hypothesis.
12. 
    
13. As such, the final conclusion is that ...
    • The sample data suggest that the populaton proportion is significantly different from 66% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer Candidate A is different from 66%
    • The sample data suggest that the population proportion is not significantly different from 66% at αα = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer Candidate A is different from 66%.

Answer 1

p: Proportion voters who prefer Candidate A

For this study, we should use : 1-PropZTest

Null hypothesis : H_o p = 0.66

Alternate Hypothesis : H_a : p 0.66

Two tailed test

Hypothesize proportion :p_o

Number of potential voters in the sample : n = 96

Number of potential voters who prefer Candidate A : x=60

Sample proportion of voters who prefer Candidate A: =x/n = 0.625

=0.10

The test statistic = -0.724

For two tailed test :

P(Z<-0.7239) = 0.2346

p-value = 2 x P(Z<-0.7239) = 0.2346 =2 x 0.2346 =0.4692

The p-value = 0.4692

As P-Value i.e. is greater than Level of significance i.e (P-value:0.4692 > 0.1:Level of significance); Fail to Reject Null Hypothesis

The p-value is greater than

Based on this, we should Fail to reject the null hypothesis:

As such, the final conclusion is that ...

• The sample data suggest that the population proportion is not significantly different from 66% at = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer Candidate A is different from 66%.