Let mu1 and mu2 denote true average densities for two differ

Let mu1 and mu2 denote true average densities for two different types of brick. Assuming normality of the two density distributions, test H0: mu1 ? mu2 = 0 versus Ha: mu1 ? mu2 not equals to 0 using the following data: m = 8, x = 24.74, s1 = 0.162, n = 7, y = 20.99, and s2 = 0.250. (Use alpha = 0.05. Round your test statistic to three decimal places and your P-value to four decimal places.) t= P-value = State the conclusion in the problem context. Reject H0. The data suggests no difference between the true average densities for the two different types of brick. Reject H0. The data suggests a difference between the true average densities for the two different types of brick. Fail to reject H0. The data suggests a difference between the true average densities for the two different types of brick. Fail to reject H0. The data suggests no difference between the true average densities for the two different types of brick.

Solution

Pooled-Variance t Test for the Difference Between Two Means

(assumes equal population variances)

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

6

Sample Mean

23.79

Sample Standard Deviation

0.162

Population 2 Sample

Sample Size

5

Sample Mean

21.95

Sample Standard Deviation

0.23

Intermediate Calculations

Population 1 Sample Degrees of Freedom

5

Population 2 Sample Degrees of Freedom

4

Total Degrees of Freedom

9

Pooled Variance

0.0381

Standard Error

0.1182

Difference in Sample Means

1.8400

t Test Statistic

15.5693

Two-Tail Test

Lower Critical Value

-2.2622

Upper Critical Value

2.2622

p-Value

0.0000

Answer

t = 15.569

P=0.0000

calculated P=0.0000 < 0.05 level of significance

Reject Ho. The data suggests a difference between true average densities for the two different type of bricks.

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	6
Sample Mean	23.79
Sample Standard Deviation	0.162
Population 2 Sample
Sample Size	5
Sample Mean	21.95
Sample Standard Deviation	0.23
Intermediate Calculations
Population 1 Sample Degrees of Freedom	5
Population 2 Sample Degrees of Freedom	4
Total Degrees of Freedom	9
Pooled Variance	0.0381
Standard Error	0.1182
Difference in Sample Means	1.8400
t Test Statistic	15.5693
Two-Tail Test
Lower Critical Value	-2.2622
Upper Critical Value	2.2622
p-Value	0.0000