Question

Discrete Components, Inc., manufactures a line of electrical resistors. Presently, the carbon composition line is producing 100 ohm resistors. The population variance of these resistors "must not exceed 4" to conform to industry standards. Periodically, the quality control inspectors check for conformity by randomly selecting 10 resistors from the line and calculating the sample variance. The last sample had a variance of 4.36. If the critical value of chi-square is 16.919 and the observed value is 15.247, the appropriate decision is to _____.

		reduce the sample size
		increase the sample size
		reject the null hypothesis
		fail to reject the null hypothesis
		do nothing

Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 38 defaulted loans. If the critical value for z is -1.282 and the observed value is -1.74, the appropriate decision is to _______.

		reduce the sample size
		increase the sample size
		reject the null hypothesis
		fail to reject the null hypothesis
		do nothing

Answer 1

(1) If the critical value of chi-square is 16.919 and the observed value is 15.247, the appropriate decision is to: fail to reject the null hypothesis.

>> As the observed value of the chi-square test does not exceed the critical value as an absolute manner, we fail to reject the null hypothesis.

(2) If the critical value for z is -1.282 and the observed value is -1.74, the appropriate decision is to: reject the null hypothesis.

>> As the observed value of the z test exceeds the critical value as an absolute manner, we reject the null hypothesis.