Question

1.Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning." These words begin a report on a statistical study of the effects of logging in Borneo. Here are data on the number of tree species in 12 unlogged forest plots and 9 similar plots logged 8 years earlier:

Unlogged	22	18	22	20	15	21	13	13	19	13	19	15
Logged	17	4	18	14	18	15	15	10	12

Use the data to give a 90% confidence interval for the difference in mean number of species between unlogged and logged plots. Compute degrees of freedom using the conservative method.

Interval: to  

2.

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. Here are data on the "penetrability" of the same type of soil at two levels of compression. Penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil.

Compressed Soil

2.8	2.69	2.97	2.82	2.76	2.81	2.78	3.08	2.94	2.86
3.08	2.82	2.78	2.98	3.00	2.78	2.96	2.90	3.18	3.16

Intermediate Soil

3.2	3.35	3.1	3.40	3.38	3.14	3.18	3.26	2.96	3.02
3.54	3.36	3.18	3.12	3.86	2.92	3.46	3.44	3.62	4.26

Use the data, omitting the high outlier, to give a 90% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. Compute degrees of freedom using the conservative method.

Interval: to  

3. A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of 2424 stores this year shows mean sales of 8585 units of a small appliance, with a standard deviation of 1313 units. During the same point in time last year, an SRS of 3030 stores had mean sales of 72.9172.91 units, with standard deviation 6.56.5 units. An increase from 72.9172.91 to 8585 is a rise of about 14%.

1. Construct a 95% confidence interval estimate of the difference μ1−μ2μ1−μ2, where μ1μ1 is the mean of this year's sales and μ2μ2 is the mean of last year's sales.

(a)  <(μ1−μ2)<<(μ1−μ2)<

(b) The margin of error is  .

2. At a 0.050.05 significance level, is there sufficient evidence to show that sales this year are different from last year?

A. Yes
B. No

Answer 1

1)

t value at 90% = 1.8595

CI = (x1 -x2) +/- t * sqrt(s1^2/n1 + s2^2/n2)
= (17.5 - 13.6667) +/- 1.8595 * sqrt(3.5291^2/12 + 4.5^2/9)
= (0.4616, 7.2051)

Interval 0.4616 to 7.2051

3)

t value at 95% = 2.0687

CI = (x1 -x2) +/- t * sqrt(s1^2/n1 + s2^2/n2)
= (85 - 72.91) +/- 2.0687* sqrt(13^2/24 + 6.5^2/30)
= (6.0765 , 18.1035)

6.0765 < mu1 -mu2 < 18.1035

b)

Margin of error = t * sqrt(s1^2/n1 + s2^2/n2)
= 2.0687* sqrt(13^2/24 + 6.5^2/30)
= 6.0138

2)
A) yes
because confidence interval does not contain 0