Question

Only 11% of registered voters voted in the last election. Will voter participation change for the upcoming election? Of the 300 randomly selected registered voters surveyed, 48 of them will vote in the upcoming election. What can be concluded at the αα = 0.01 level of significance?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
2. The null and alternative hypotheses would be:   

H0:H0:  ? μ p  Select an answer = < ≠ >   (please enter a decimal)   

H1:H1:  ? p μ  Select an answer < = ≠ >   (Please enter a decimal)

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly different from 11% at αα= 0.01, so there is statistically insignificant evidence to conclude that the percentage of registered voters who will vote in the upcoming election will be different from 11%.
   • The data suggest the populaton proportion is significantly different from 11% at αα = 0.01, so there is statistically significant evidence to conclude that the the percentage of all registered voters who will vote in the upcoming election will be different from 11%.
   • The data suggest the population proportion is not significantly different from 11% at αα= 0.01, so there is statistically significant evidence to conclude that the percentage of registered voters who will vote in the upcoming election will be equal to 11%.

Answer 1

Solution :

p = 11% = 0.11

Claim : Will voter participation change for the upcoming election?

n = 300 , x = 48 α = 0.01 , p^ = x / n = 48/300 = 0.16

1. For this study, we should use

z-test for a population proportion

2. The null and alternative hypotheses would be:   

H0: p = 0.11  

H1: p ≠ 0.11

The test statistic ?

z = (p^-p)/√(p(1-p))/n

= (0.16-0.11)/√((0.11*(1-0.11))/300

= 2.768

z = 2.768

The p-value =  0.0056

The p-value is ≤ α

Based on this, we should

reject the null hypothesis

Thus, the final conclusion is that ...

• The data suggest the populaton proportion is significantly different from 11% at α = 0.01, so there is statistically significant evidence to conclude that the the percentage of all registered voters who will vote in the upcoming election will be different from 11%.