Two alloys A and B are used in the manufacture of steel bars

Two alloys, A and B, are used in the manufacture of steel bars. suppose a steel producer wants to compare the two alloys on the basis of average load capacity, defined as the maximum load (weight in tons) it can support without breaking. steel bars containing alloy A and steel bars containing alloy B were randomly selected and tested for load capacity. the results are summarized in the table:

a) Find a 99% confidence interval for the difference between the true mean load capacities for the two alloys, M(A) - M(B).

b) State the assumptions you are making to justify the inference derived in (a)

c) Is it plausible to assume that the true population means, M(A) and M(B), are in fact equal? WHY?

Alloy	Sample Size	Mean	Variance
A	11	43.7	48.5
B	17	48.5	19.9

Solution

Two alloys, A and B, are used in the manufacture of steel bars. suppose a steel producer wants to compare the two alloys on the basis of average load capacity, defined as the maximum load (weight in tons) it can support without breaking. steel bars containing alloy A and steel bars containing alloy B were randomly selected and tested for load capacity. the results are summarized in the table:

Alloy

Sample Size

Mean

Variance

A

11

43.7

48.5

B

17

48.5

19.9

Population 1 Sample

Sample Size

11

Sample Mean

43.7

Sample Standard Deviation

6.964194

Population 2 Sample

Sample Size

17

Sample Mean

48.5

Sample Standard Deviation

4.46094

Intermediate Calculations

Population 1 Sample Degrees of Freedom

10

Population 2 Sample Degrees of Freedom

16

Total Degrees of Freedom

26

Pooled Variance=(10*48.5+16*19.9)/26 =

30.9000

Standard Error = sqrt( 30.9(1/11+1/17))=

2.1510

Difference in Sample Means

-4.8000

Degrees of Freedom

26

t Value at 99%

2.7787

Interval Half Width=2.151*2.7787=

5.9770

Confidence Interval

Interval Lower Limit =(-4.8-5.977) =

-10.7770

Interval Upper Limit=(-4.8+5.977) =

1.1770

99% confidence interval = (-10.777, 1.177)

The samples are random and independent.

The samples come from normal populations with equal variances.

c) Is it plausible to assume that the true population means, M(A) and M(B), are in fact equal? WHY?

The true population means, M(A) and M(B), are in fact equal because the 99% confidence interval contains 0.

Alloy	Sample Size	Mean	Variance
A	11	43.7	48.5
B	17	48.5	19.9