statistics assignment #4.

Assignment #4

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.

Tests on Variances, Goodness-of-Fit and Independence

8. In order to estimate the effectiveness of thinning, five plots were established in thinned and unthinned stands (on similar sites and in similar forest types). On each plot, the volume increment per year per hectare was measured. The results follow:

Volume Increment (m3/hectare/year)
Thinned	Unthinned
8	9
6	4
5	4
10	6
11	2

1. Estimate the real standard deviation in the thinned stand with 90% confidence limits.

2. Using the proper technique, find out if the real variances from both stands are similar or significantly different, with 90% confidence.

9. A coin is tossed until a tail occurs and the number of tosses, X, is recorded. The experiment is repeated 256 times and the following data are obtained.

X	1	2	3	4	5	6	7	8 or more
f	136	60	34	12	9	1	3	1

1. Name the distribution of the random variable X and write the general formula for it.

2. Test the hypothesis, at the 0.05 level of significance, that the observed distribution of X may fit the distribution you named in part (a).

10. The following table shows the distribution for a random sample from the lengths in millimeters of Douglas-fir cones.

Class Limits	Frequency
50	8
51-70	17
71-90	31
91-110	27
111-130	12
131	5

Test the hypothesis (α = 0.05) that the distribution from which this sample comes is normal.

11. An analysis of accident data was made to determine the distribution of numbers of fatal accidents for drivers under 25. The data for 299 accidents are as follows:

12.	Fatal	Not Fatal
Female	26	128
Male	43	102

Do the data indicate that the frequency of fatal accidents is dependent on sex? Use α = 0.05.

13. The grade distributions of FRST 130 (final mark) for three previous years are given in the following table:

14.	Fail	50 – 64%	64 – 79%	80 – 100%
1975-76	9	16	26	32
1976-77	6	35	37	8
1977-78	6	28	20	9

Are the grade distributions independent of year (class)? Draw your conclusion using 0.01 level of significance.