Maths Question on Tensile Strength?

Question

below gives the tensile strength of a sample of 80 steel cables.

Breaking Strength (Frequency)

(In Newtons)

20.0 (3)

25.0 (5)

30.0 (23)

35.0 (35)

40.0 (10)

45.0-50.0 (4)

Total ( 80 )

Calculate the mean standard deviation of the breaking strength

Also a small sample of steel cables were tested later to check for consistency giving the following tensile strengths;

25.1, 31.8, 40.9, 28.3, 32.8, 36.7

Calculate the mean tensile strength of this second sample.

Giving that the standard deviation of this data is 5.68 newtons, how do the tensile strengths compare?

Answer 1

FORMULAE

WEIGHTED MEAN  (EXPECTED VALUE)

μ = Σx * P(X = x)

GROUPED DATA VARIANCE

Var(X) = σ² = Σ(x - μ)² * P(X = x) = {Σx² * P(X = x) }- μ²

GROUPED DATA STANDARD DEVIATION

s = SQUARE ROOT[σ²]

Weighted Statistics

Mean     StDev

33.625   6.09149

MEAN TENSILE STRENGTH OF SECOND SAMPLE = 32.6

TEST CONCERNING TWO MEANS, INDEPENDENT SAMPLES, UNPOOLED t-DISTRIBUTION, 5% SIGNIFICANCE LEVEL

Two samples are not comparable.  They are more different than is tolerable to a 5% significance level