a) Give a 95% upper confidence bound for the expected value of the contaminant c

Question

a) Give a 95% upper confidence bound for the expected value of the contaminant content. b) Give a 90% symmetrical confidence interval for the variance of the measurement. 3. A company requires raw material that has high enough tensile strength. The material is acceptable only if the tensile strength is greater than 300 N/mm2. This is of great importance so the test should be carried out so that the unacceptable material is rejected with 95% probability. When deciding whether a batch of material should be accepted 8 samples were taken, and the measurements were 303.8 N/mm 2 should be used? Why? Perform the test and decide whether the batch should be accepted. tensile strength was measured. The average and standard deviation of the and 5.10 N/mm2 respectively. What kind of statistical test l The ields of the runs

Explanation / Answer

Question 3

H0 : = 300 N /mm2

Ha :   > 300 N /mm2

Sample size = 8

sample mean x = 303.8 N/mm2

sample standard deviation s = 5.10 N/mm2

Here we will use one sample t - test for hypothesis testing.

here

standard error of the sample mean se0 = s/ sqrt(n) = 5.10 / sqrt(8) = 2.8284

t = (x - H )/se0

t = (303.8 - 300)/ 2.8284 = 1.3435

here p - value = 0.1105

so here p - value > 0.05, which is significance level here. So we shall not reject the null hypothesis and we can conclude reject the batch as it is less than 95% probable that tensile strength of the batch is greater than 300 N/ mm2

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