Question

38- Problem The "fun size" of a Snickers bar is supposed to weigh 20 grams. Because the penalty for selling candy bars under their advertised weight is severe, the manufacturer calibrates the machine so the mean weight is 20.I grams. The quality-control engineer at M&M-Mars, the Snickers manufacturer, is concerned about the calibration. He obtainsa random sample of 11 candy bars, weighs them, and obtains the data bellow. Should the machine be shut down and calibrated? Because shutting down the plant is very expe he decides to conduct the test at the α 0.01 level of significance. (15 pt.) nsive, 9.98_| 20.55-121.501 20.6612065|20·36.119.74-119.56.119.6 1 | 21.02

Answer 1

Following table shows the calculations:

	X	(X-mean)^2
	19.68	0.385641
	19.98	0.103041
	20.55	0.062001
	21.5	1.437601
	20.66	0.128881
	20.65	0.121801
	20.36	0.003481
	19.74	0.314721
	19.56	0.549081
	19.61	0.477481
	21.02	0.516961
Total	223.31	4.100691

Sample size Sample sum 1-223.31 riok: ikari 2 -223.31/11 -20.301 Sample standard deviation: :sqrt(4.100691/(11-1)) ー 7 =0.6404

Hypotheses are: Level of significance: α-0.05 Test is one tailed (left tailed) df -n-1-10 Degree of freedom: Test Statistics: =(20.301-20)/(0.6404/sqrt(11)) 1.559 Critical value: CV --1.812 Rejection Region: If t<-1.812, Reject HO Decision: Since test statistics does not lie in rejection region so we fail to reject the null hypothesis p-value: P-value-0.075 Decision: Since p-value is not less than level of significance so we fail to reject the null hypothesis Excel function for critical value: Excel function for p-value: =TINV(0.1, 10) =TDIST( 1.559, 10, 1)