Q1. A pistachio rancher buys a new fertilizer system that is supposed to increase the yield per acre. She uses the system for one year and notes the following output per acre:
71.7 46.0 103.9 54.4 43.3 68. 1 73.4 45.1 45.6 44.9 77.8 50.5
a) Calculate the Average yield per acre
b) Calculate the Standard deviation
Q2. Explain the difference between a one sample and a two sample hypothesis test; provide an example of each.
Q3. One-Sample Tests of Hypothesis:
- State the null and alternative hypothesis
- State the decision rule
- Calculate the appropriate test statistic,
- Indicate your decision regarding H0
To help the Greasy Spoon restaurant manager target the correct age levels, you want to find if there is a statistically significant difference @ the 5% level between the age of the restaurant customers and the local population, which is 43.1 years. A random sample of 50 customers shows an average age of 33.6 years with a SD of 16.2 years.
Q4. Correlation and Regression Analysis:
The owner of a financial services firm believes that there is a relationship between the number of client contacts and the dollar amount of sales. He gathered the following sample information. The X column indicates the number of client contact last month, and the Y column shows the value of sales ($ thousand) last month for each client sampled
|
Number of Contacts (X)
|
Sales ($ thousand)(Y)
|
|
|
|
|
14
|
24
|
|
|
|
|
12
|
14
|
|
|
|
|
20
|
28
|
|
|
|
|
16
|
30
|
|
|
|
|
46
|
80
|
|
|
|
|
23
|
30
|
|
|
|
|
48
|
90
|
|
|
|
|
50
|
85
|
|
|
|
|
55
|
120
|
|
|
|
|
50
|
110
|
|
|
|
Find the coefficient of correlation:
Find the coefficient of determination and non-determination.:
Find the regression equation (Y=a + bX):
Determine the estimated sales if 37 contacts are made.
Q5. Two Sample Test of Hypothesis- Unpaired test of Hypothesis t-test
Gender Discrimination? Your firm is being sued for gender discrimination and you are asked to evaluate the data. There appears to be a highly significant difference between men's and women's salaries. The table below presents the findings:
DATA WOMEN MEN
Sample size 15 22
Average salary $24, 467 $33,095
Standard deviation 2,806 4,189
Standard error 724 893
The issue is whether the difference in salary is within the usual random variation or not. The question is whether such a large difference in salary could be the result of a random allocation of salaries or if there is a need for some other explanation for the apparent inequity.
- State the null and alternative hypothesis
- State the decision rule
- Calculate the appropriate test statistic,
- Indicate your decision regarding H0