Answer the questions below using the appropriate statistical technique. For ques

Question

Answer the questions below using the appropriate statistical technique. For questions in- volving the use of hypothesis testing, you must:
-State the null and research hypotheses
-Provide the Z(critical), T(critical), or 2(critical) score corresponding to the thresh- old for your test
-Provide your test statistic
-Provide your decision about statistical significance
You must also substantively interpret the results of your test (but keep it short). That is, don’t just focus on whether or not a test is statistically significant, but also briefly comment on what the result actually means. You may find it helpful to proceed using the five-step model, but this is optional. Be sure to select a test that is appropriate given the question, and decide whether the question calls for a one-tailed or two-tailed test.

3. An insurance company wants to know whether perceptions of personal health are in- dependent of gender. The company has hired you as a statistical consultant. You then collected a random sample of people and asked about their perceived health status. Based on the results of this survey, is the sex of the respondent independent from their perceived health status? Use 95% confidence. (1 point)

Perceived Health Status
Women Men
Very Good 89 121

Good 82 65

Not so good 42 30

  

Explanation / Answer

here we will apply chi square test of independence.

null hypothesis: perceived health status and gender are independent.

alternate hypothesis: perceived health status and gender are dependent

critical value of X2 for 2 degree of freedom =5.9915

as test stat 8.822 is higher then critical value , we reject null hypothesis and conclude that perceived health status is dependent of gender

Observed O male Female Total very good 89 121 210 good 82 65 147 not so good 42 30 72 Total 213 216 429 Expected E=rowtotal*column total/grand total male Female Total very good 104.266 105.734 210 good 72.986 74.014 147 not so good 35.748 36.252 72 Total 213 216 429 chi square =(O-E)^2/E male Female Total very good 2.235 2.204 4.439 good 1.113 1.098 2.211 not so good 1.093 1.078 2.171 Total 4.442 4.380 8.822

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