Question

A sample of 565 low-income and 680 high-income individuals was surveyed concerning their opinions on television violence. Among the low-income respondents, 400 believed that television violence is excessive, whereas 417 of the high-income respondents believed that television violence is excessive. Answer the following questions.

1. What is the null hypothesis? (1 point) 2. What is the research hypothesis? (1 point) 3. What is the proportion for each group? (2 point) 4. What is the z-statistic for the test? (2 points) 5. Using formal sentences, explain the results of the hypothesis test of the difference between the two proportions (alpha=.05). Use numbers to support your conclusion. (4 points)

Answer 1

(1) The Null Hypothesis: H0: p1 = p2

(2) The Alternative Hypothesis: Ha = p1 p2 : Claim

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(3) The proportions

= Sample Proportion of low income individuals = 400/565 = 0.708

= Sample Proportion of high income individuals = 417/680 = 0.6132

p = pooled Proportion = (400 + 417) / (565 + 680) = 817 / 1245 = 0.6562

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(4) The test Statistic:

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(5) The p value at z(3.51) is 0.0004.

The critical values at = 0.05 are 1.96 and -1.96

The Decision rule is that if p value < 0.05, Reject H0.

Also if z observed is > 1.96 or if z observed is < -1.96, Reject H0.

Since p value is < 0.05, and Z statistic is > 1.96, We reject H0

The Conclusion is : Reject the null Hypothesis. There is sufficient evidence at the 95% level of significance to support the claim that there is a difference in proportions between the low income and high income individuals who believe that television violence is excessive.

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