Question

About one year 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 54% of Virginians would support this legalization.  To test this claim she collected a random sample of 382 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.”

Obtain the sample proportion of individuals who said “Support” using Stat àTables àFrequency in StatCrunch.  Only the value of the sample proportion is needed in your answer.  Present this sample proportion as a fraction or a decimal rounded to 4 decimal places.

Frequency table results for Opinion:
Count = 382

Opinion	Frequency	Relative Frequency
0	169	0.4424
1	213	0.5576

1- Using a= 0.05, is there sufficient evidence to conclude that more than 54% of Virginia adults support legalized sports betting?  Conduct a full hypothesis test by following the steps below.

A-Define the population parameter in one sentence.

B-State the null and alternative hypotheses using correct notation.

C-State the significance level for this problem.

D- Check the three conditions of the Central Limit Theorem that allow you to use the One-Proportion z-Test using one complete sentence for each condition.  Show work for the numerical calculation.

E- Calculate the test statistic “by-hand.”  Show the work necessary to obtain the value by typing your work and provide the resulting test statistic.  Do not round while doing the calculation.  Then, round the test statistic to two decimal places after you complete the calculation.

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

G- State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence (compare your p-value to the significance level to do this).

H- 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

1- Using a= 0.05, is there sufficient evidence to conclude that more than 54% of Virginia adults support legalized sports betting?  Conduct a full hypothesis test by following the steps below.

A-Define the population parameter in one sentence.

proportion of all individuals who said Support legalized sports betting

B-State the null and alternative hypotheses using correct notation.

Ho: P=0.54, H₁: P>0.54

Upper tail test

C-State the significance level for this problem.

significance level = 0.05

D- Check the three conditions of the Central Limit Theorem that allow you to use the One-Proportion z-Test using one complete sentence for each condition.  Show work for the numerical calculation.

Sample collected are random.

Sample proportion p=213/382 =0.5576

Both np=382*0.5576 =213 and n(1-p)=382*(1-0.5576) =168.9 > 10, normal approximation is appropriate.

E- Calculate the test statistic “by-hand.”  Show the work necessary to obtain the value by typing your work and provide the resulting test statistic.  Do not round while doing the calculation.  Then, round the test statistic to two decimal places after you complete the calculation.

=0.6899

z= 0.69 ( two decimals)

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

P= 0.2451

G- State whether you reject or do not reject the null hypothesis and the reason for your decision in one sentence (compare your p-value to the significance level to do this).

Since calculated P=0.2451 > 0.05 level of significance, Ho is not rejected.

H- 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.

There is not enough evidence to conclude that more than 54% of Virginia adults support legalized sports betting.