1. Write a null and an alternative hypothesis for each of the following. Be sure to state each hypothesis in the context of the problem.
A. A forestry textbook claims that the mean age of pine trees in Colorado is 30 years. You think the age is greater than that. (2 points)
ans: Ho = mean = 30
the mean age of the pine trees is 30 years for Ho
Ha : mean > 30
the mean age of pine trees is more than 30 years
B. A brochure on anti-aging cream states that the mean age of people in the United States is 75 years. You doubt the claim, and you think it's greater because the information is out of date and the population of the elderly is growing. (2 points)
ans: Ho = mean = 75
for Ho the mean age of people in US is 75 years
Ha : mean > 75
for Ha. The mean age of ppl in US is greater than 75 years
C. A fisheries report states that the mean weight of trout in Lake Standarderror is 3.4 pounds. You think the information is out of date, and that the population may have changed. (2 points)
Ho: mean = 3.4
The mean weight of trout is 3.4 pounds
Ha: mean ≠ 3.4
The mean weight is not 3.4 pounds
D. Acme Caterpillar Farm claims the mean length of their award-winning caterpillars is 8 centimeters. You've seen their caterpillars and you think the mean length must be shorter. (2 points)
Ho: mean = 8
Mean length of caterpillars is 8 centimeters
Ha: mean < 8
Mean length of caterpillars is less than 8 centimeters.
2. A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard deviation of .4 billion years. (Their ages are approximately normally distributed.) You think the mean age is actually greater, and that this would lend support to an alternative theory about how the clusters were formed. You use a computer to randomly select the coordinates of 50 stars from the catalog of known stars of the type you're studying and you estimate their ages. You find that the mean age of stars in your sample is 3.4...
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