All hypothesis tests must be done using the p-value method only State the hypoth

Question

All hypothesis tests must be done using the p-value method only

State the hypothesis, significance level, test statistic, p-value, decision and conclusion

8.16 Surface roughness of pipe. Refer to the Anti-corro Methods and Materials (vol. 50, 2003) study of the sur- face roughness of coated interior pipe used in oil fields, Exercise 7.24 (p. 284). The data (in micrometers) for 20 sampled pipe sections are reproduced in the table a. Give the null and alternative hypotheses for testing whether the mean surface roughness of coated interior pipe, Au, differs from 2 micrometers. b. Find the test statistic for the hypothesis test. c. Give the rejection region for the hypothesis test, using d. State the appropriate conclusion for the hypothesis test e. In Exercise 7.24 you found a 95% confidence interval for u. Explain why the confidence interval and test sta- tistic lead to the same conclusion about u. ROUGH PIPE 1.72 2.50 2.16 2.13 1.06 2.24 2.31 2.03 1.09 1.40 2.57 2.64 1.26 2.05 1.19 2.13 1.27 1.51 2.41 1.95 Source: Farshad F., and Pesacreta, T. "Coated pipe interior surface roughness as measured by three scanning probe instruments." Anti corrosion Methods and Materials vol. 50, No. 1, 2003 (Table III)

Explanation / Answer

Detailed Statistics of a given sample

a. Null HYpothesis : H0 : Mean surface thickness = 2.00 mm

Alternative Hypothesis : Ha : Mean surface Thickness 2.00 mm

b. test statistics = (xbar-   )/ (s/n) = (1.88- 2.00)/ (0.5239/20) = (-0.12)/ 0.1171 = -1.0248

c.   Here tcriticalvalue for dF = 20 -1 = 19 for significance level alpha = 0.05

tcritical = -2.093

d. HEre t < tcritical so Here we cannot reject the null hypothesis and we can conclude that mean surface roughness of coated interior pipe is equal to 2.00 mm

e. 95% confidence interval for

=> 95% confidence interval = xbar+- t/2,19 (s/n)

= 1.88 +- 2.093 * (0.5239/20)

95% CI = (1.635, 2.125)

we can say that the mean = 2.00 mm is given under the 95% CI. so it can be true that mean surface roughness of interior is equal to 2.00 mm.

Surface Roughness Mean (xbar) 1.881 Standard Error 0.117150151 Median 2.04 Mode 2.13 Standard Deviation 0.523911403 Sample Variance 0.274483158 Kurtosis -1.35025677 Skewness -0.275115175 Range 1.58 Minimum 1.06 Maximum 2.64 Sum 37.62 Count 20 Confidence Level(95.0%) 0.245198084

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