Question

Only 12% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 321 randomly selected registered voters surveyed, 51 of them will vote in the upcoming election. What can be concluded at the αα = 0.10 level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for a population mean

The null and alternative hypotheses would be:   

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

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

The test statistic ? z t  =  (please show your answer to 3 decimal places.)

The p-value =  (Please show your answer to 4 decimal places.)

The p-value is ? ≤ >  αα

Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.

Thus, the final conclusion is that ...

The data suggest the population proportion is not significantly higher than 12% at αα = 0.10, 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 12%.

The data suggest the populaton proportion is significantly higher than 12% at αα = 0.10, 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 higher than 12%.

The data suggest the population proportion is not significantly higher than 12% at αα = 0.10, so there is statistically insignificant evidence to conclude that the percentage of registered voters who will vote in the upcoming election will be higher than 12%.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.12
Alternative Hypothesis, Ha: p > 0.12

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1589 - 0.12)/sqrt(0.12*(1-0.12)/321)
z = 2.145

P-value Approach
P-value = 0.0160
As P-value < 0.1, reject the null hypothesis.

The data suggest the populaton proportion is significantly higher than 12% at αα = 0.10, 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 higher than 12%.