Help please? The research department of your local state representative wants to

Question

Help please? The research department of your local state representative wants to know if there is a difference in the voting habits of Republicans vs. Democrats. A random sample of 400 Republicans revealed 120 voted in the last election Similarly, a sample of 600 Democrat revealed that 150 had voted in the last election At the 05 significance level, is there a significant difference in the proportions of the voting liabits of Republicans vs. Democrats? Use the five-step hypothesis testing procedure. 1. Step 1. What is the hypothesis? 2. Step2. What is the significance level? 3. Step 3. What is the Rejection Region. (Given)step4, if the P_c is-p_c = 120 + 150/400 + 600 = 0.27 z compute out to be 1.74 z= 0.30 - 0.15/squareroot (0.27)(0.73)/400 + (0.27)(0.73)/600 = 1.74 4. Step 5. What is your decision regarding Ho based on the decision rule (rejection region)? 5 What is the p-value? 6 What is your conclusion based on p-value 7 What can you conclude?

Explanation / Answer

1.

Ho: There is no significance difference in the proportions of the voting habits of Republicans vs Democrats

H1: There is significance difference in the proportions of the voting habits of Republicans vs Democrats

2.

For this test the level of significance is 0.05.

3.

Here alternative hypotheisis is not simple so rejection region have two parts so we say that type of test is two tailed test.

4.

If z claculated value is less than the tabulated value of the standred normal variate table then we accept the null hypothesis other wise we reject the null hypothesis.

5.

calculated z- value is 1.74 here we use the R- software to calculate the p- value

P- value <- 2*pnorm(-abs(1.74),lower.tail=T) # R code for calculating P- value when z- value kmow

P- value = 0.0818

6.

Another way we take a decisions on the basis of the p- value , if calculated p- value is less than 0.05 i.e level of significance then we reject the null hypothesis. here P-value is greater than 0.05 so we accept the null hypothesis for the given data set

7.

On the basis of test we conclude that, There is no significance difference in the proportions of the voting habits of Republicans vs Democrats. i.e both parties are having approsimate equal proportion of voters.

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