(1) What are the steps involved in hypothesis testing? How do you decide what the null hypothesis is? When would you reject a null hypothesis? if you were unable to reject the null hypothesis, what would be its implications?
(2) The average work week for Americans is claimed to be 43 hours nationally. To test this figure, a local leisure product marketer randomly selects 44 sales people and asks them to keep a log book of hours worked. Suppose the sample average turns out to be 40.5 hours with a standard deviation of 9 hours. Using the hypothesis testing procedure (show all steps and use 95 % confidence) what can the marketer infer/conclude?
(3) In 2013, the average number of years passenger cars were being used was 6.5 years. In 2014, a sample of 100 passenger cars showed a sample mean of 7.8 years and a sample standard deviation of 2.2 years.
(a) Formulate the null and alternate hypotheses
(b) Use a .01 level significance and test the hypotheses
(c) What implication does this have for vehicle manufacturers.
(4) A car manufacturer introduces a new method of assembling a particular component. The old method had a mean assembly time of 42 minutes. The manufacturer would like the assembly time to be as short as possible, and so he expect the new method to have a smaller mean. A random sample of assembly times (minutes) taken after a new method had become established was
27 39 28 41 42 35 32 38
stating any necessary distributional assumptions, investigate the manufacturer's expectation.
(5) A random sample of 15 workers from a vacuum flask assembly line was selected from a large number of such workers. Ivor Stopwatch, a work study engineer, asked each of these workers to assemble a one-litre vacuum flask at their normal working speed. The times taken, in seconds, to complete these tasks are given below.
109.2 146.2 127.9 92 108.5
91.1 109.8 114.9 115.3 99
112.8 130.7 141.7 122.6 119.9
Assuming that this sample came from an underlying normal population, investigate the claim that the population mean assembly time is less than 2 minutes.
(6) In processing grain in the brewing industry, the percentage extract recovered is measured. A particular brewing introduces a new source of grain and the percentage extracted on 11 separate days is as follows:
95.2 93.1 93.5 95.9 94 92 94.4 93.2 95.5 92.3 95.4
Test the hypothesis that the true mean percentage extract recovered is 95. What assumptions have you made in carrying out your test?
(7) Please interpret the SAS statistical output (you don't need to know SAS to interpret the output, I am trying to see whether you can make sense of confidence interval, mean, std deviation, standard error, degrees of freedom, P value, t value- do you really know what they mean? This is what I am interested in)
N 7 Mean 75.7143 Std Dev 8.4007 Std Err 3.1752
Minimum 63.0000 Maximum 85.0000
95% CL Mean 67.9450 83.4836
95% CL Std Dev 5.4133 18.4989
DF 6 t 3.88 Value Pr> |t| 0.0082'
For the hypothesis test with p = 0.05 (95% confidence interval).... How do you interpret the results?
(8) A meat processing company in the Midwest produces and markets a package of eight small sausage sandwiches. The product is nationally distributed, and the company is interested in knowing the average retail price changed for this item in stores across the country. The company can not justify a national census to generate this information. The company information system produces a list of all retailers who carry the product. A researcher for the company contacts 36 of these retailers and ascertains the selling prices for the product. Use the following price data to determine a point estimate for the retail price of the product. Construct a 90 % confidence interval to estimate this price:
|
2.23
|
2.11
|
2.12
|
2.2
|
2.17
|
2.1
|
|
2.16
|
2.31
|
1.98
|
2.17
|
2.14
|
1.82
|
|
2.12
|
2.07
|
2.17
|
2.3
|
2.29
|
2.19
|
|
2.01
|
2.24
|
2.18
|
2.18
|
2.32
|
2.02
|
|
1.99
|
1.87
|
2.09
|
2.22
|
2.15
|
2.19
|
|
2.23
|
2.1
|
2.08
|
2.05
|
2.16
|
2.26
|
(9) A university has 15,000 students. We have drawn a simple random sample of size 400 from the population, and recorded how much money each student spend on cellular telephone service during November, 2003. For this sample, the sample mean is $36, and sample standard deviation is $20. At a 99% level of confidence, test the null hypothesis that these 15,000 students, combined, did not spend more than $500,000 on cellular telephone service during November, 2003.
(10) Please identify the problems with each of the following survey questions. And , explain why you think that it is the problem... what are the consequences of asking these questions?
(a) what do you think of the taste and texture of this Sara Lee coffee cake?
(b) Don't you agree that Dell computers are the best by all measures
(c) We are conducting a study for Marriott Hotel: What do you think of the hotel?
(d) How would you characterize your consumption of beer?