Question

Only 16% of registered voters voted in the last election. Will voter participation decline for the upcoming election? Of the 347 randomly selected registered voters surveyed, 45 of them will vote in the upcoming election. What can be concluded at the αα = 0.05 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  ? ≠ > < =   (please enter a decimal)   

H1:H1:  ? p μ  ? ≠ = < >   (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 accept fail to reject reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly lower than 16% at αα = 0.05, 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 16%.
   • The data suggest the population proportion is not significantly lower than 16% at αα = 0.05, so there is statistically insignificant evidence to conclude that the percentage of registered voters who will vote in the upcoming election will be lower than 16%.
   • The data suggest the populaton proportion is significantly lower than 16% at αα = 0.05, 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 lower than 16%.

Answer 1

a) z-test for a population proportion

b) against

c) Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic

d) P-value

e) P-value <

f) Since P-value < , so we reject  the null hypothesis.

g) The data suggest the population proportion is significantly lower than 16% at αα = 0.05, 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 lower than 16%.