Question

1. Two samples are taken with the following sample means, sizes, and standard deviations

¯x1 = 31 ¯x2 = 35
n1= 73   n2= 67
s1= 2 s2 = 5

Estimate the difference in population means using a 99% confidence level. Use a calculator, and do NOT pool the sample variances. Round answers to the nearest hundredth.
_____< μ1−μ2 <_____

2. You are conducting a test of independence for the claim that there is an association between the row variable and the column variable.

	X	Y	Z
A	27	33	48
B	12	35	46

What is the chi-square test-statistic for this data? Round to 3 decimal places
χ2=_____

3. You are conducting a test of homogeneity for the claim that two different populations have the same proportions of the following two characteristics. Here is the sample data.

Category	Population #1	Population #2
A	6	6
B	52	51

What is the chi-square test-statistic for this data? Report to 3 decimal places
χ2=______

Answer 1

1)

The confidence interval for difference in means is obtained using the formula,

Where,

The degree of freedom is obtained using the formula,

The t critical value is obtained from t distribution table for significance level = 0.01 and degree of freedom = 85.12

2)

The observed values are,

Observed values
	X	Y	Z	Total
A	27	33	48	108
B	12	35	46	93
Total	39	68	94	201

The expected values are obtained using the formula,

Expected values
	X	Y	Z	Total
A				108
B				93
Total	39	68	94	201

The Chi-Square Value is obtained using the formula

Observed,	Expected,
27	20.96	6.04	36.54	1.74
33	36.54	-3.54	12.51	0.34
48	50.51	-2.51	6.29	0.12
12	18.04	-6.04	36.54	2.02
35	31.46	3.54	12.51	0.40
46	43.49	2.51	6.29	0.14
				4.778

3)

The chi-square test for homogeneity can be used here to determine whether the several populations are equal or homogeneous in some characteristics

he Chi-Square test statistic is obtained as follow,

The observed values are,

Observed values
	Population 1	Population 2	Total
A	6	6	12
B	52	51	103
Total	58	57	115

The expected values are obtained using the formula,

Expected values
	X	Y	Total
A	6.05	5.95	12
B	51.95	51.05	103
Total	58	57	115

The Chi-Square Value is obtained using the formula

Observed,	Expected,
6	6.0522	-0.0522	0.0027	0.0004
6	5.9478	0.0522	0.0027	0.0005
52	51.9478	0.0522	0.0027	0.0001
51	51.0522	-0.0522	0.0027	0.0001
				0.001