Question

A researcher has selected a random sample of 120 older residents (age 65+) in Nebraska and asked them how many times they’ve been victimized by crime in the past year. He found that the senior citizens averaged 2.8 victimizations last year. The researcher also has information on the amount of victimization experienced in the entire state. On average, the population of Nebraskans experienced 2.4 victimizations last year, with a standard deviation of 2.7. The researcher wonders whether senior citizens are victimized at a different rate than the general state population. Run the appropriate one-sample hypothesis test (with alpha = .05) to answer the research question.

Your work shown must include:

i. verifying that the assumptions are met.

ii. listing the null hypothesis and the research hypothesis.

iii. computing the appropriate test statistic.

iv. identifying the degrees of freedom (if necessary) and p-value v. writing a complete interpretation of the test and results.

show all work, no outside sources

Answer 1

(i) Assumptions:

(a) The sample is a simple random sample

(b) The samples are independent of each other.

(c) Since the sample size is large, we can assume normality.

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(ii) The Hypothesis:

H0: = 2.4

Ha: 2.4

This is a 2 tailed test

(iii) The Test Statistic: Since the population standard deviation is known and n > 30, we use the z test.

The test statistic is given by the equation:

(iv) The p Value: The p value (2 Tail) for Z= 1.62, is; p value = 0.1052

The Decision Rule: If P value is < , Then Reject H0.

The Decision:   Since P value (0.1052) is > (0.05) , We Fail to Reject H0.

The Conclusion: There isn't sufficient evidence at the 95% significance level to conclude that there is a difference in the rates at which senior citizens of Nebraska are victimized from the General Population.

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