Question

Prior to a local election, you would like to estimate the percentage of voters that are in favor of a 4% increase in gasoline sales tax in order to generate enough revenue for street repair. You decide to take a random sample of 400 local voters to see if at least 60% of voters support this initiative. Use this information to answer question 1a to 1e. (Hint: recall that for a Bernoulli random variable, the standard deviation is p(1 – p).) In your survey, you determine that 273 voters are in favor of the 4% increase to the gasoline sales tax. Determine the value of the test statistic for your hypothesis test. (Use 3 decimal places) Determine the P value. (Use 4 decimal places) Assume that the true proportion of voters who are against the sales tax increase is 41%. What is the power of your hypothesis test? (Use 4 decimal places)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.6
Alternative Hypothesis, Ha: p > 0.6

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.6825 - 0.6)/sqrt(0.6*(1-0.6)/400)
z = 3.368

P-value Approach
P-value = 0.0004