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1 . The hourly wages in a particular forest industry are normally distributed with a mean of $13.20 and a standard deviation of $2.50. If a company in this industry employing 40 summer students

16 / 01 / 2019 Statistics

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Hypothesis Testing on Means and Proportions

1    . The hourly wages in a particular forest industry are normally distributed with a mean of $13.20 and a standard deviation of $2.50. If a company in this industry employing 40 summer students pays these students on the average $12.20, can this company be accused of paying inferior wages to the students? Use α = 0.05.


2    . The drained weights in ounces for a sample of fifteen cans of fruit are given below. At the 1% level of significance, test the hypothesis that on the average a twelve-ounce drained weight standard is being maintained, against the alternative that it is not twelve ounces.

12.1    12.1    12.3    12.0    12.1
12.4    12.2    12.4    12.1    11.9
11.9    11.8    11.9    12.3    11.8

                
3. A study was conducted to determine whether the engineers have a greater annual income ten years after graduation than do foresters. Random samples were taken from each group with the following results (measured in $1,000s):
Annual Income, in $1000s

Engineers    Foresters
n1 = 38    n2 = 34
x̄1 = 38.65    x̄2 = 35.94
S1 = 6.4    S2 = 5.5

Test your hypothesis at the 0.05 probability level.
4.    A regeneration survey has indicated that 85 of the 110 plots examined were stocked. If the requirement is 80% stocking for satisfactory regeneration, would you call this area as "satisfactory"? Use α = 0.01.

5.    Another survey from another area indicated 84% stocking from 100 plots. Is this area different from the area described in Question (4)? Use α = 0.05.

6.    If the germination capacity of a seed lot is at least 70%, it is acceptable for a nursery. A test of a given seed lot showed that 8 out of 18 seeds germinated. Would you accept this seed lot? Use α = 0.05 (or as close as possible). 

7.    Discuss the differences and/or similarities in general between interval estimation and test of hypothesis.




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