Question 2 Prior to a local election, you would like to estimate the percentage

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Question 2 Prior to a local election, you would like to estimate the percentage of voters that are in favor of a 4% in gasoline sales tax in 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 2a to 2g. (Hint: recall that for a Bernoulli random variable, the standard deviation is VP(- ) Question 2a: What type of hypothesis test are you conducting? (select all that apply) One mean Two mean unpaired Two mean paired One-sided lower tail One-sided upper tail Two sided test t test Question 2b: In your survey, you determine that 263 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)

Explanation / Answer

Solution

(a) Hypothesis test is :

(b) Here, null hypothesis H0 : p=0.6

alternate hypothesis H1 : p>=0.6

sample proportion = 263/400 = 0.6575

z test statistic = (pbarp0)/sqrt(p0(1p0)/n)

=(0.6575-0.6)/((0.6)(0.4)/400)0.5 = 2.347

(c) Z value at 2% significance level = 2.054

Reject H0 (z critical value < z test statistic)

(d) P value : P(Z>2.347) = 0.0095

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