A manufacturer of concrete bridge supports is interested in determining the effect of varying the sand content of concrete on the strength of the supports. Five supports are made for each of five different amounts of sand in the concrete mix and each support tested for compression resistance. The compression resistance results are recorded in the table below.

Percent Sand Compression Resistance (10,000 psi) mean(yi) StDev(si)

15 7 7 10 15 9 ____ _____

20 17 12 11 18 19 _____ _____

25 14 18 18 19 19 _____ _____

30 20 24 22 19 23 ______ _____

35 7 10 11 15 11 _______ _____

a. Identify the response variable.

b. Identify the factor variable and list the factor levels.

c. Specify H0 and Ha hypotheses for testing if the sand content of concrete affects the strength of the supports.

d. Is the data balanced? What are sample sizes?

e. Find the mean and standard deviation for each sample. (note you can use R function mean( ) and sd( ) to calculate)

f. Calculate the pooled sample variance. (We know pooled sample variance is an unbiased estimator of the common population variance)

g. Calculate the variance of sample means. (We know for balanced data, the variance of sample means multiplying the common sample size n is also an unbiased estimator of the common population variance under H0)

h. Compare these two types of variances (in f and g), do you favor to reject H0? Justify your answer clearly.