Question

In: Statistics and Probability

The compressive strength of concrete is being studied, and four different mixing techniques are being investigated....

The compressive strength of concrete is being studied, and four different mixing techniques are being investigated. The following data have been collected to test if the mixing techniques affect the strength of the concrete.

Mixing Technique	Compressive strength (psi)
A	3125	3200	2800	2600
B	3000	3300	2900	2700
C	2865	2975	2985	2600
D	2890	3150	3050	2765

a. Find the summary statistics for compressive strength of each mixing technique.

b. State the null and alternative for the above problem.

c. What assumptions are required to perform the hypothesis testing for above problem?

d. Is there any evidence that mixing techniques affect the strength of the concrete at 5% level of significance?

Expert Solution

a. Plot comparative boxplot for each type of mixing techniques and interpret the results (use Excel/R to draw the plots).

There is equal variance among the groups.

b. Find the summary statistics for compressive strength of each mixing technique.

Mean	n	Std. Dev
2,932.0	4	281.60	A
2,975.0	4	250.00	B
2,856.3	4	179.28	C
2,963.8	4	170.36	D
2,931.8	16	207.08	Total

c. State the null and alternative for the above problem.

The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

d. What assumptions are required to perform the hypothesis testing for above problem?

Normality – That each sample is taken from a normally distributed population.
Sample independence – that each sample has been drawn independently of the other samples.
Variance Equality – That the variance of data in the different groups should be the same.

e. Is there any evidence that mixing techniques affect the strength of the concrete at 5% level of significance?

Source	SS	df	MS	F	p-value
Treatment	34,379.50	3	11,459.833	0.23	.8766
Error	6,08,875.50	12	50,739.625
Total	6,43,255.00	15

The p-value is 0.8766.

Since the p-value (0.8766) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that mixing techniques affect the strength of the concrete.

orchestra answered 2 years ago

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