Two materials are compared with respect to their compressive strengths. The foll

ID: 2921138 • Letter: T

Question

Two materials are compared with respect to their compressive strengths.

The following data were gathered:

Material Compressive strength One 755:4 788:3 734:3 721:4

Two 535:1 628:7 542:8 559:3 1.

The two material measurements are independent. Explain why. [1 mark]

2. Provide an estimate of the mean di§erence in compressive strength between the two materials. [4 marks]

3. Calculate and interpret a 98% conÖdence interval for the mean di§erence in compressive strength between the two materials. [15 marks]

4. Use a 0.02 significance level and the following points to test the claim that Material Two has a lower compressive strength than Material One.

(a) State the null and alternative hypotheses in symbolic form and in context.

(b) Calculate the test statistic. (c) Identify the rejection region(s). (d) Clearly state your conclusions (in context). [5 marks each]

following data has been conceived from the given question and using ms-excel following information has been generated

(2) mean difference=749.5-566=183.5

(3) (1-alpha)*100% confidence interval for difference =difference ±t(alpha/2,n1+n2-2)*SE(difference)

=183.5±t(0.2/2,6)*25.81=183.5±3.14*25.81=183.5±81.04=(102.46, 264.54)

(4) we use t-test and

(a) null hypothesis H0: mean two = mean One

alternate hypothesis H1: mean two<mean One

t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2

( c) one tailed critical t(0.02,6)=2.61 , so critical region t>2.61

(d) since the test statistic belongs to critical region, so we reject null hypothesis and conclude that mean two is less than me

one two 755 535 788 628 734 542 721 559 mean= 749.5 566 s= 29.24038303 42.54409477 n= 4 4

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