Answer to Question #105332 in Statistics and Probability for Katenda

Question

Question 14

What is the decision with regard to the hypothesis and the conclusion about the population mean?
(1) We reject the null hypothesis and conclude that the population mean is equal to 100.
(2) We reject the null hypothesis and conclude that the population mean is not equal to 100.
(3) We do not reject the null hypothesis and conclude that the population mean is equal to 100.
(4) We do not reject the null hypothesis and conclude that the population mean is not equal to
100.
(5) We accept the null hypothesis.

Question 17

Consider a Chi-square random variable with 15 degrees of freedom and 0.1 level of significance.
Which of the following test statistic values will result in rejection of the null hypothesis?
(1) 21.1
(2) 18.5
(3) 19.8
(4) 23.5
(5) 2.7

Answer 1

Question 14

If the calculated value falls in the critical region, We reject the null hypothesis and conclude that the population mean is not equal to 100.

Question 17

Consider the critical values

Left sided: =CHISQ.INV(0.1,15)=8.45

Right sided: =CHISQ.INV(0.9,15)=22.31

Two sided =CHISQ.INV(0.05,15), =CHISQ.INV(0.95,15)= (7.26,24.996)

The formulas used are excel formulas.

From left sided test, any value less than 8.45 leads to rejection. On right sided test, any value greater than 22.31 leads to rejection of the null hypothesis. Based on the two sided test, any value less than 7.26 or greater than 24.996 leads to rejection. Thus, the value 2.7 leads to rejection under left sided test while 23.5 leads to rejection under right sided test. On two sided test, the value 2.7 leads to rejection of the null hypothesis