Question

Part B (Based off week 11 workshop content) An engineering company has ordered steel to be used for a rail construction project. Before using the steel, they want to test it to ensure the material properties from the supplier are correct. A random sample of the ordered steel is tested for its Yield Strength. The results are shown below. Yield Strength (MPa) 197 203 194 196 196 197 198 205

1. Calculate the sample mean and sample variance by hand, then verify your answers with MATLAB’s mean and var functions.

2. The supplier claims that the average Yield Strength of their steel is 200 MP a. Conduct a hypothesis test to determine whether there is enough evidence to reject this claim using a significance level of α = 0.05.

3. Determine a 95% confidence interval for the average Yield Strength. Does the confidence interval support the result of your hypothesis test?

4. Use the ttest function in MATLAB to verify your answers to Q2 and Q3. 5. If we were to double the sample size and obtain the same sample mean and sample variance, what would happen to the 95% confidence interval for Yield Strength? Explain why this happens.

Answer 1

0) 147 198 205 97 203 94 16 PT 98.5718 Somple vosiome m 드 (197-198.57山3)t(203-198.6714354 t 3.112 8ST

2) MATLAB CODE 47,20, 9 6,27,198,20S ChiP, ci, Stats: ttef (x) OUTPUT anjue 148.5 tlo J200 tia: 200 wit unKnoon Populotion 8tandosd dleviatbn Rejetian Region proviied , the -Sign逝cance evold: 0.05 and

is tc2-365 The sedtion eos this tu's tailed testu R.t m»23453 ふ 드 198.2 S_2co 8-77018377 -1313 De cision o bout nusl hupcthesis: Since it s observed tht 1313te 2.86S it then conluted that the nlpotikas is not gede The p-valua P 02306, and Sirn P 0 23062 005, it i covrtucled thc the hutl hyrothesis s not ogeted. it conckued thot the null

(3 inknesi, CCnJ İdare, The 95-1. 2 198.25 (MPa) デニ 9S. 09TS

L.S) 95 091s Ma, 201-402S M gince he infervet includes the tfue 2co aniene ntena cenain the J5 th team in dknminrin msgin otesh J2n 962s to05 2n- 2n 198.2.5土2.132衹3-77018 16 - 98 25+ 2. 009S I(196 20,200.255