Explanation to "Test of hypothesis" question

10.10 In an attempt to improve quality many manufacturers are developing partnerships with their suppliers. A local fast-food burger outfit has partnered with its supplier of potatoes. The burger outfit buys potatoes in bags that weigh 20 lbs. It wishes to set up the null and alternative hypotheses to test if the bags do weigh on the average 20 lb.

10.11 You are a connoisseur of chocolate chip cookies and you do not think that Nabisco's claim that every bag of Chips Ahoy cookies has 1000 chocolate morsels is correct. Set up the null and alternative hypotheses to test this claim.

10.23 In an attempt to improve quality, many manufacturers are developing partnerships with their suppliers. A local fast-food burger outfit has partnered with its supplier of potatoes. The burger outfit buys potatoes in. bags that weigh 201b. It does not wish to accept underweight bags of potatoes. A sample shows an average weight of 19.95 lb with a standard deviation of O.1 Ib.

(a) Set up the null and the alternative hypotheses to test if the average bag weighs at least 20 lb.
(b) Test your hypothesis using a = 0.05.
(c) Find the p value.
(d) Based on the p value, should the burger outfit accept the shipment of potatoes?

12.15 Most traffic lights are set so that there is enough time for pedestrians to cross the road safely. A recent study indicates that a large number of elderly cannot get across the road in the usual 15 seconds allowed. To determine the average amount of time it takes senior citizens to cross the street, a study was taken of 25 seniors. On the average it took them 19.5.seconds to cross the street, with a sample standard deviation of five seconds. Assume the time to cross the road has a normal distribution.

(a) Set up the null and alternative hypotheses to see if the data show that it does indeed take seniors longer than15 seconds to cross the street.

(b) In terms of traffic flow, what are the implications of a Type I error?

(c) What are the implications of a Type II error?

(d) Find the value of the test statistic.

(e) If a = 0.05, what is the rejection region?

(f) What is your recommendation to the city?

12.22 Look again at your recommendation to the city about the length of its walk light signal. In writing your report, you start to think about whether or not the study you did was ad equate.

(a) What other factors might be useful in determining the length of time to allow people to cross the street safely?

(b) What are the drawbacks of making decisions such as this based on the mean?

(c) What might be a better statistic to use in this case?