Question

Q: Assistance to understand clearly and solve this example from Probability and Statistical Inference with the steps of the solution to better understand, thanks.

**Please give the step by step with details to completely see how the solution came about, plenty of thanks.

1) A random sample of 48 women who were test for cholesterol was classified according to age an cholesterol level and grouped into the following contingency table:

age	<=210	>210	Totals
<50
>=50

Test the null hypothesis $H_{0}$ that age and cholesterol level are independent attributes of classification of the 1% significance level.

What is the distribution for the statistic Q?

a) F(2,2)

b) X²(1)

c) X²(2)

d) X²(4)

24 17

Answer 1

Date: 23/04/2019 Answer The distribution for the statistics Q is chi-square. The degree of freedom is, d,f.= (r-1): (c-1) -(2-1)x (2-1) The answer is b To test the hypothesis is that age and cholesterol level are dependent at 1% significance level. The null and alternative hypothesis is, The null hypothesis is that age and cholesterol level are independent The alternative hypothesis is that age and cholesterol level are dependent.

The chi-square statistics is. By using Excel software, find chi-square test statistics with the help of following steps 1)Import the data 2)Select Contingency table from Chi-Square in MegaStat option from Add-Ins menu 3) Select Chi-Square and Expected frequencies in Output options 4) Click Ok Chi-square Contingency Table Test for Independence -210 16 11.50 Total 24 24.00 24 24.00 >210 <50 Observed Expected 50 Observed Expected Total Observed Expected 12.50 17 12.50 25 25.00 11.50 23 23.00 48.00 6.762 chi-square 1 df 0093 p-value From the Excel output, the chi-square test statistic is 6.762

The p-value is, From the Excel output, thep-value is 0.0095. The p-value is 0.0095 Decision The conclusion is that the significant p-value is less than 0.01 which is 0.0095, so the null hypothesis is rejected at 1% level of significance. There is sufficient evidence to indicate that age and cholesterol level are dependent. The result is statistically significant