Question

Problem 2: Virginia Sports Betting

Several years ago, polling numbers began to show that public opinion about legalizing sports betting had changed. For the first time, a majority of Americans supported making wagering on professional sports legal. A researcher in the state of Virginia is currently interested in this topic. She wants to test the claim that more than 62% of Virginians support this legalization. To test this claim she collected a random sample of 107 Virginia adults and then asked whether they support or oppose legalized professional sports betting. The responses (0 = Oppose and 1 = Support) are found in StatCrunch in a data set called “Virginia Sports Betting Survey.”

Opinion:
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1

a) Define the population parameter in context in one sentence.

b) Frequency table results for Opinion: Count = 107

Opinion	Frequency	Relative Frequency
0	31	0.2897
1	76	0.7103

c) State the null and alternative hypotheses the researcher wishes to test using correct notation.

d) State the significance level for this problem.

e) Check the three conditions of the Central Limit Theorem that allow you to use the oneproportion z-test using one complete sentence for each condition. Show work for the numerical calculation. You can assume the population is large.

f) Calculate the test statistic “by-hand.” Show the work necessary to obtain the value by typing all the steps needed and the resulting test statistic. Do not round while doing the calculation. Then, round the test statistic to two decimal places.

g) Calculate the p-value using the standard Normal table and provide the answer. Use four decimal places for the p-value.

h) State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence.

i) Based on your above decision, state your conclusion in context of the problem (i.e. interpret your results and/or answer the question being posed) in one or two complete sentences.

Answer 1