Question

Only 18% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 365 randomly selected registered voters surveyed, 84 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:  ? μ p  ? = < ≠ >   (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 reject fail to reject accept  the null hypothesis.

Answer 1

Solution :

This is the right tailed test .

(a)

z-test for a population proportion

(b)

The null and alternative hypothesis is

H0 : p = 0.18

Ha : p > 0.18

= x / n = 84 / 365 = 0.2301

(a)

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.2301 - 0.18 / [(0.18 * 0.82) / 365]

z = 2.493

(b)

P-value = 0.0063

(c)

= 0.05

P-value

(d)

Reject the null hypothesis .