Question

A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ 64, Let μ denote the true average compressive strength

Answer 1

For first question sample size is needed.

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Second:

Hypotheses are:

Ho : μ = 200 . Ha : μ 200

Degree of freedom: df=n-1=29

The p-value using excel function "=TDIST(5.874,29,2)" is 0.0000

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Third

Following is the output of descriptive statistics:

Descriptive statistics
	X
count	5
mean	2,886.00
sample standard deviation	79.04
sample variance	6,248.00
minimum	2789
maximum	3005
range	216

So,

Here we have T-2886,s -79.04, n-5 Hypotheses are: Ho 3000 Ha: μ# 3000 Level of significance: .05 Test is two tailed. Degree of freedom df -n-1-4 Test Statistics: (2886-3000)/(79.04/sqrt(5)) -3.225 Critical value: 2.776 Rejection Region: If t >2.776, Reject HO Decision: Since test statistics lies in rejection region so we reject the null hypothesis P-value: P-value-0.0321 Decion e prahue s pothesi Excel function for critical value TINV(0.05,4) Excel function for p-value: -TDIST(3.225,4,2)