Question

Only 14% of registered voters voted in the last election. Will voter participation decline for the upcoming election? Of the 365 randomly selected registered voters surveyed, 44 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 t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:   

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

  

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

3. The test statistic ? t z  =  (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 14% 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 14%.
   • The data suggest the populaton proportion is significantly lower than 14% 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 lower than 14%.
   • The data suggest the population proportion is not significantly lower than 14% 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 lower than 14%.

Hint:
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Answer 1

a)

z tets for a population proportion

b)

Null Hypothesis, H0: p >= 0.14
Alternative Hypothesis, Ha: p < 0.14

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1205 - 0.14)/sqrt(0.14*(1-0.14)/365)
z = -1.074

d)

P-value Approach
P-value = 0.1414

e)

As P-value >= 0.01,

f)

fail to reject null hypothesis.

G)

The data suggest the population proportion is not significantly lower than 14% 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 lower than 14%.