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MATHS - Four Problems

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solution.


Question

1. The gestation period of gray squirrels in captivity is listed as 44 days. It is recognized that the potential life span of animals is rarely attained in nature, but the gestation period could be either shorter or longer. Suppose the gestation period of a sample of 81 squirrels living in the wild is measured and the mean length of gestation time is 42.5 days. Test the hypothesis that squirrels living in the wild have the same gestation period as those in captivity at the 0.05 level of significance. Assume that ? = 5 days. Use the four step process for Hypothesis Testing. (8 points)

 

 

 

 

Step 1 – State Hypothesis in context of the problem.

 

 

Step 2 – Gather data, check assumptions, and find rejection region using ?.

 

 

Step 3 – Calculate the appropriate test statistic and p-value.

 

 

Step 4 – State conclusion in context of the problem.

 

 

 

 

2. The dollar value of a college education is often measured by comparing the average annual pay for workers who were graduated from college to pay earned by those who never attended college after receiving a high school diploma. Data from the Census Bureau shows average earnings in 1996 of male workers who earned a bachelor’s degree was $53,102 and that of male high school graduates with no college experience was $34.034. Suppose a random sample of 150 male college graduates with bachelor’s degrees was taken in 1998 to check for possible salary increase and the sample mean was $53,500. That the hypothesis that no increase in average salary occurred during the 2-year period at the 0.05 level of significance. Assume ? = $3900. Use the four step process for Hypothesis Testing. (8 points)

 

 

 

 

3. The manager at Air Cargo feels that the weights of packages shipped recently are less than in the past. Records show that in the past packages have had a mean weight of 36.7 lb. and a variance of 201.64 lb2. A random sample of last months shipping yielded a mean weight of 32.1 lb. for 64 pounds. Is this sufficient evidence to reject the null hypothesis in favor of the manager’s claim? Use ? = 0.01 Use the four step process for Hypothesis Testing. (8 points)

 

 

4. A fire insurance company felt that the mean distance from a home to the nearest fire department in a suburb of Chicago was at least 4.7 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 4.7 miles. This, they felt, would convince the insurance company to lower its rates. They randomly identify 64 homes and measured the distance to the nearest fire department for each. The resulting sample mean was 4.4. If ? = 2.4 miles, does the sample show sufficient evidence to support the community’s claim at ? = 0.05 level of significance? Use the four step process for Hypothesis Testing. (8 points)

 

Paper#62258 | Written in 05-Mar-2016

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