Show your work. Cary\'s out all calculations to at least 3 significant digits. A

Question

Show your work. Cary's out all calculations to at least 3 significant digits. A manufacturer of TV sets claims that at least 98% of its TV sets can last more than 10 years without needing a single repair. In order to verify and challenge this claim, a consumer group randomly selected 800 consumers who had owned a TV set made by this manufacturer for 10 y ears. Of these 800 consumers. 60 said that their TV sets needed some repair at least once. Is there significant evidence showing that the manufacturer's claim is false? Test using a - 0.01. Do the data show that the manufacturer's actual no-repair rate does not even reach 95%? Use a = 0.01 A company selling licenses of new e-commerce software advertised that firms using this software could obtain, on average during the first year, a minimum yield (in cost savings) to 20 percent on average on their software investment. To disprove the claim, we checked with 10 different firms which used the software. These firms reported the following cost-saving yields (in percent) during the first year of their operations: {17.0, 19.2. 21.5. 18.6. 22.1. 14.9. 18.4. 20.1. 19.4, 18.9}. Compute a 95% confidence interval for the average cost-saving yield estimate. Do we have significant evident to show that the software company's claim of a minimum of 20 percent in cost savings was not valid? Test using a = 0.05.

Explanation / Answer

1.1) here phat =740/800=0.925

also calimed p=0.98

hence std error =(p(1-p)/n)1/2 where n=800

=0.0049

hence test stat z =(phat-p)/std error =(0.925-0.98)/0.0049=-11.22

for which p value =0.0000

as p value is less then both 0.01 and 0.05 we reject claim of manufacturer at both level (a) and b

1.2) here mean =20

from sample

here degree of freedom =n-1=9

for 9 df and 95% CI, t=2.262

hence confidence interval =sample mean +/- t*std error =17.528 ; 20.492

b) as out confidence interval contains 20 as a possible mean value ; we can not reject company's claim

X 17.000 19.200 21.500 18.600 22.100 14.900 18.400 20.100 19.400 18.900 mean(X) 19.010 std deviation(S) 2.071 std error =S/(n)1/2 0.655

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