Exercise 1 :Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet....

Exercise 1 :Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet. Shown are the cholesterol readings in millimoles per litre (mmol/L) of the 11 employees both before the new diet and one month after use of the diet began. Construct a 98% confidence interval to estimate the population mean difference of cholesterol readings for people who are involved in this program. Assume differences in cholesterol readings are normally distributed in the population. Employee Before After 1 6.59 5.09 2 5.95 5.82 3 7.50 5.56 4 6.26 5.56 5 7.76 6.21 6 6.46 6.08 7 5.56 4.91 8 5.95 6.21 9 5.82 5.17 10 5.66 5.25 11 6.10 5.77

Exercise 2: Is there a significant difference in the fuel efficiency of a car for regular unleaded and premium unleaded gas? To test this hypothesis, an analyst randomly se- lected 15 drivers for a study. They were to drive their cars for one month on regular unleaded and for one month on premium unleaded gas. The participants drove their own cars for this experiment. The average sample difference was 1.32L/100 km in favour of the premium unleaded, and the sample standard devia- tion of difference was 2.08 L/100 km. For α = 0.01, does the test show enough evidence for the analyst to conclude that there is a significant difference in fuel efficiency between regular unleaded and premium unleaded gas? Assume the differences in fuel efficiency figures are normally distributed in the population.

Exercise 3:

Figures from Statistics Canada show that the average size of Canadian farms has increased since 1956. In 1956, the mean size of a farm was 122 ha; by 2011, the average size was 315 ha. Between those years, the number of farms decreased but the amount of tillable land remained relatively constant, so now farms are bigger. This trend might be explained, in part, by the inability of small farms to compete with the prices and costs of large-scale operations and to produce a level of income necessary to support the farmers’ desired standard of living. Suppose an agri-business analyst believes the average size of farms has now increased from the 2011 mean figure of 315 ha. To test this notion, she randomly sampled 23 farms and ascertained the size of each one from county records. The data she gathered follow. Use a 5% level of significance to test her hypothesis. Assume that the number of hectares per farm is normally distributed in the population.

298 327 317 337 369 319 303 310 312

373 335 301 293 334 312 319 373 289

364 342 395 375 375

Exercise 4:

The Bureau of Labor Statistics in the U.S. shows that the average insurance cost to a company per employee per hour is $1.84 for managers and $1.99 for profes- sional specialty workers. Suppose these figures were obtained from 35 managers and 41 professional specialty workers, and that their respective populations are normally distributed with standard deviations $0.38 and $0.51.

1. Calculate a 98% confidence interval to estimate the difference in the mean hourly company expenditures for insurance for these two groups.

2. Determine whether there is a significant difference in the hourly rates employers pay for insurance between managers and professional specialty workers. Use a 2% level of significance.

Feb 02, 2023

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Exercise 1 :Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet....

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