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Assignment Questions

A market research study is designed to determine if more than 25% of the residents of a large city would be a new type of cereal. A random sample of 600 people is selected and is given the new cereal to try. The 600 people are then asked if they would buy this cereal and 168 responded they would. At α = 0.05, is there enough evidence to conclude that more than 25% of the residents of this city would buy the new type of cereal? Use the p-value

A company that manufactures pavers used in residential landscaping. The company guarantees that the paver average weight is no more than 10kg. However, recently the company has received many complaints that the pavers are heavier than expected. In an effort to address the customers complaints, the quality control manager selected a random sample of 40 pavers. The average and standard deviation obtained from this sample are 10.3kg and 3.1 kg, respectively. At α = 0.10, can it be concluded the pavers average weight is higher than 10kg? Use the critical value/rejection point

A new hip replacement procedure is being evaluated at a big research hospital. This new procedure is less expensive; however, it might lead to a longer recovery time. A study was conducted to compare this new procedure with the current procedure. A randomly sample of 15 patients were operated on with the current procedure, and another sample of 12 patients were operated with the new procedure. The average and standard deviation of the recovery time for the sample that was treated with the current procedure are 35 days and 7.5 days, respectively. The average and standard deviation for the recovery time for the sample that was operated with the new procedure 39 days and 6.2 days, respectively. Is there enough evidence to conclude that, on average, patients who undergo a hip replacement using the new procedure need more time to recover? Test at α = 0.01. Use the critical value/rejection point

A researcher wants to test the claim that women who are exposed glycol ethers are more likely to have miscarriages than those who are not. Among the 40 women who are exposed glycol ethers that he randomly selected, 15 had miscarriages. Whereas, among the randomly selected 780 women who are not exposed glycol ethers, 130 had miscarriages. Is there enough evidence to conclude that the claim is correct? Use α = 0.01. Use the p-value method.

Do left-hand and right-hand average reaction times differ? To test this, 12 right-handed subjects were randomly selected and the reaction times of their right and left hands, in thousands of seconds, were recorded. The following table contains the results.

Subject

1

2

3

4

5

6

7

8

9

10

11

12

Right

189

96

112

166

115

131

169

158

110

102

182

157

Left

222

168

188

205

195

168

178

169

138

186

152

218

At α = 0.10, test the claim that there is a difference in the average reaction times of the left and right hands. Use the p-value method.

A fish-processing company is concerned about the shelf life of its new cat food. A random sample in Halifax and another sample in Dartmouth were examined. The results are summarized below.

Halifax

Dartmouth

Sample Size

35

40

Sample Mean (months)

13

11

Sample Standard Deviation

1.44

1.52

Is there a difference in the average shelf life between the two locations? Conduct a hypothesis test 0.05 significance level. Use the critical value/rejection point method.

A group of university students are interested in comparing the average age of cars owned by students and the average age of cars owned by faculty. They randomly selected 25 cars that are own by students and 20 cars that are owned by faculty. The average age and standard deviation obtained from the students’ cars are

6.78 years and 5.21 years, respectively. The sample of faculty cars produced a mean and a standard deviation of 5.86 years, and 2.72.

A). Construct and interpret a 90% confidence interval for the difference between the average age of students’ cars and average age of faculty

B). At α = 0.05, is there enough average to conclude that on average faculty cars are newer than students’ cars? Use the p-value method.

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