Question

Flu

0-18 years 7

19-34 years 22

35-49 Years 40

50-64 Years 57

65 years or older 61

Total Cases 187

The age distribution has 20% of its citizens under the age of 18 and 13% over the age of 65.

Using this information, answer the following questions. Back up your conclusions with an appropriate test. To receive full credit, include the test statistic, p-value, expected counts and conclusion in plain English.

1. Does the age distribution statistically differ from the age distribution of the county?

2. Is there statistical evidence that people under the age of 18 are less affected?

Answer 1

Answer 1

Assume a level of significance of 5%.

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0: The age distribution is same as the age distribution of the country i.e. p1 =0.2, p2 =0.223333, p3​=0.223333, p4​=0.223333, p5 =0.13 Ha​: Some of the population proportions differ from the values stated in the null hypothesis This corresponds to a Chi-Square test for Goodness of Fit. (2) Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df=n-1=5-1=4, so then the rejection region for this test is R={χ2:χ2>9.4877}. (3) Test Statistics The Chi-Squared statistic is computed as follows: (4)P-value The P-value is the probability that a chi-square statistic having 4 degrees of freedom is more extreme than 9.4877. The p-value is p=Pr(χ2>95.0705)=0 (5) Decision about the null hypothesis Since it is observed that χ2=95.0705>χc2​=9.4877, it is then concluded that the null hypothesis is rejected. (6) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level. Hence the age distribution does statistically differ from the age distribution of the country. Conditions a. The sampling method is simple random sampling. b. The variable under study is categorical. c. The expected value of the number of sample observations in each level of the variable is at least 5.

The test run in excel with comprehensive formulas is:

Answer 2

Yes, there seems to be statistical evidence that people under the age of 18 are less affected. This is because the contribution of the people under age of 18 to the chi-square statistic is very significant at 24.7102.

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