10. A federal agency responsible for enforcing laws governing weights and measur

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10. A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is not less than the advertised figure on the package. A random sample of 18 containers whose packaging states that the contents weigh 8 ounces was drawn. The contents were weighed and the results follow. Can we conclude at the 1% significance level that on average the containers are mislabelled (i.e. average weight is less than 8 ounces)? Use the rejection region approach and remember to check the possible assumptions. 7.807.917.937.997.947.757.977.957.79 8.067.827.897.927.877.927.988.057.91 -------------------------------------------------------------- 11. University bookstores order books that instructors adopt for their courses. The number of copies ordered matches the projected demand. However, at the end of the semester the bookstore has too many copies on hand and must return them to the publisher. A bookstore has a policy that the fraction of books returned should be kept as small as possible. The average is supposed to be less than 10%. To see whether the policy is working, a random sample of book titles was drawn and the fraction of the total originally ordered that are returned is recorded and listed here. Can we infer at the 10% significance level that the mean fraction of returns is less than 10%? Use the rejection region approach and remember to check the possible assumptions. 415117594358 10. A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is not less than the advertised figure on the package. A random sample of 18 containers whose packaging states that the contents weigh 8 ounces was drawn. The contents were weighed and the results follow. Can we conclude at the 1% significance level that on average the containers are mislabelled (i.e. average weight is less than 8 ounces)? Use the rejection region approach and remember to check the possible assumptions. 7.807.917.937.997.947.757.977.957.79 8.067.827.897.927.877.927.988.057.91 -------------------------------------------------------------- 11. University bookstores order books that instructors adopt for their courses. The number of copies ordered matches the projected demand. However, at the end of the semester the bookstore has too many copies on hand and must return them to the publisher. A bookstore has a policy that the fraction of books returned should be kept as small as possible. The average is supposed to be less than 10%. To see whether the policy is working, a random sample of book titles was drawn and the fraction of the total originally ordered that are returned is recorded and listed here. Can we infer at the 10% significance level that the mean fraction of returns is less than 10%? Use the rejection region approach and remember to check the possible assumptions. 415117594358 10. A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is not less than the advertised figure on the package. A random sample of 18 containers whose packaging states that the contents weigh 8 ounces was drawn. The contents were weighed and the results follow. Can we conclude at the 1% significance level that on average the containers are mislabelled (i.e. average weight is less than 8 ounces)? Use the rejection region approach and remember to check the possible assumptions. 7.807.917.937.997.947.757.977.957.79 8.067.827.897.927.877.927.988.057.91 -------------------------------------------------------------- 11. University bookstores order books that instructors adopt for their courses. The number of copies ordered matches the projected demand. However, at the end of the semester the bookstore has too many copies on hand and must return them to the publisher. A bookstore has a policy that the fraction of books returned should be kept as small as possible. The average is supposed to be less than 10%. To see whether the policy is working, a random sample of book titles was drawn and the fraction of the total originally ordered that are returned is recorded and listed here. Can we infer at the 10% significance level that the mean fraction of returns is less than 10%? Use the rejection region approach and remember to check the possible assumptions. 415117594358

Explanation / Answer

Data:    

n = 18   

= 8   

s = 0.085   

x-bar = 7.914   

Hypotheses:    

Ho: 8   

Ha: < 8   

Decision Rule:    

= 0.01   

Degrees of freedom = 18 - 1 = 17

Critical t- score = -2.566933975   

Reject Ho if t < -2.566933975   

Test Statistic:    

SE = s/n = 0.085/18 = 0.020034692

t = (x-bar - )/SE = (7.914 - 8)/0.0200346921336188 = -4.292554107

Decision (in terms of the hypotheses):

Since -4.292554107 < -2.566933975 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that < 8 ounces

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