Question

US manager of a plant hos. of X, the number of emnt- 15. A machine dispenses a liquid drug deviation of the contents is 54 milliliter containers and the standard deviation for At the 5% level of significance, test the claim that the amounts dispenscu - 8 - ne dispenses a liquid drug into bottles in such a way that the standard I the contents is 54 milliliters. A new machine is tested on a sample of 24 1s and the standard deviation for this sample group is found to be 21 milliliters. machine have a smaller standard deviation (use 2 - distribution for analysis) (7 points). 16. The Bank of New England is concerned about the amount of debt being accrued by customers using its credit cards. The Board of directors decided to install an expensive monitoring system if the mean for all of the bank's customers is greater than $2000. The bank randomly selected 100 credit card holders and determined the amounts they charged. For this sample group the mean is $2177 and standard deviation is $843. Use 0.025 level of significance to test the claim that the mean amount charged is greater than $2000. Based on the results of testing, will the monitoring system be implemented? (7 points)

Answer 1

15)

Claim: The amount dispensed by the new machine have a smaller standard deviation.

Sample size = n = 24

Sample standard deviation = s = 21

The null and alternative hypothesis is

H0:σ 54

H1 :σ< 54

Test statistic is

$(1 – u) =zY

(24-1)+ 21: 542

10143 x=0016 -=3.478

Critical value = 35.172

( From chi-square table)

Test statistic < Critical value we fail to reject the null hypothesis.

Conclusion:

The amount dispensed by the new machine has NOT a smaller standard deviation.