Question

3. A machine produces metal rods used in an automobile suspension system. A random sample of 12 rods is selected and the diameter is measured. The resulting data in mm, are shown here: 8.23 8.29 8.19 8.14 8.31 8.19 8.29 8.32 8.42 8.24 8.30 8.40 Find a two-sided 95% confidence interval for the mean rod diameter. State the assumption necessary to find the confidence interval. (5 marks) Is there any evidence to indicate that mean rod diameter exceeds 8.20 mm using significance level -0.05?. Write the appropriate hypothesis. Make required assumption(s) (5 marks)

Answer 1

Sisu Sun & Confidence interval for mean 't distribution t-n e tons [nu.degree of freedo ] PC It < Genua, key] =1-4 P[- temu, ale) < n-M <tem, an] =1-4 P [ in s tem, ale <H4 nt s temiyases J = 1-2. (1-2) 100% confidence limits for u are (u s t (n=1,112, n + s temu, ale)) Here , n = 12 u &ni= 1 (8.23 + 8-314 ... (.40] =8.28 Santa E(Xi-v - 2 = 0.007 t ( 11,0.os) = 2.20 cafidence intowel: (2.28 - 0722-20 , 9128 to 1412-70) C.I. = (8.27554, 8.284446). Ho: M=8. 20 Ja=0.05 VIS Hi: u> 8.20 t- u-u so toll I slun Assumptions. (both cases) Parent population is normal. In sample observations are independent ii) Population Standard deviation is unknown.