Hypothesis Testing Problems

MLB 1
A study was conducted to determine if persons in surburan district I have a different mean income from those in district II. A random sample of 50 homeowners was taken in district I. Although 50 homeowners were to be interviewed in district II also, one person refused to provide the information requested. So only 49 observations were obtained from District II. The data produced sample means and variances as shown below. Use these data to test if mean incomes for the two districts are different. Use alpha = .05. Give results f test and p-value.

District I District II
Sample Size 50 49 97
Sample Mean (in thousands $) 14.27 12.78
Sample Variances 8.74 6.58

MLB 2
The variability in the potency of five grain aspirin tablets differs from one brand to another. An interest research group would like to compare brand C, a new product recently released, to brand B the current best seller. Random samples of 41 tablets are obtained from bottles of each of the brands. The potency results are given in the table below. Use these data to test the hypothesis that the population variances of brands B and C are not equal and that the alternative hypothesis is that brand B has more variability in potency than brand C. Use alpha = .01

Need to give 3 answers:
1. Value of calculated statistic.
2. Value of critical statistic
3. Result of hypothesis test
Brand B Brand C

Sample Size 41 41
Sample Mean 60.2 60.5
Sample Variance 2.2 0.98

MLB3
A total of 210 emphysema patients entering a clinic over a one year period were treated with one of two drugs (A,B) for a period of one week. After this period of time each patient's condition was rated as either greatly improved, improved, or no changed. See table below for results. Are the patients rating dependent upon the drug product used? Create contingency table and give results of test. Alpha = .05.

Patient Condition
Drug No Change Improved Greatly Improved
A 20 35 45
B 15 45 50