Question

1. A mechanical engineer is analyzing tensile strength of steel ( API 5L X65). A sample of 7 specimens showed a sample mean of 530 M P a. The standard deviation is known to be σ = 5 M P a. A 95% upper confidence interval for the true mean tensile strength is:

2. The Z critical value that should be used in order to create a 95% lower confidence interval is:

3: For an automated bottle filling, a 95% upper confidence interval of fill volume is ( 489 , ∞ ) milliliters. How could you best describe the confidence interval?

- The true mean fill volume is less than or equal to 489 milliliters for 95% of the bottles

-The true mean fill volume is greater than or equal to 489 milliliters for 95% of the bottles

-The true mean fill volume is greater than or equal to 489 milliliters for 5% of the bottles

4. The pH value of 5 water samples taken from a small lake follow: 7.3, 7.6, 7.2, 7.9, and 7.8. The true standard deviation of water of the lake is unknown. A 95% upper confidence interval for the pH is:

5. You need to test if the water in the small lake described in question (04) is basic, i.e. if the pH is significantly greater than 7.0. The correct form of the Null and Alternative hypotheses are:

6. This question is worth 2 points: A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is Normally Distributed with σ = 0.001 millimeters. A random sample of 15 rings has a mean diameter of 74.036 millimeters. Test if the true mean ring diameter is significantly greater than 74.035 millimeters. Select the correct interpretation of the test result:

- We have NO statistical evidence with 95% probability to conclude that the true mean ring diameter is significantly greater than 74.035 millimeters.

-We have statistical evidence with 95% probability to conclude that the true mean ring diameter is significantly greater than 74.035 millimeters.

-We have NO statistical evidence with 95% probability to conclude that the true mean ring diameter is significantly equal to 74.035 millimeters.

7.A machine produces metal rods used in an automobile suspension system. A random sample of 15 was selected, and the diameter is measured. The sample mean diameter was found to be 8.24 millimeters. The true standard deviation of the diameters is maintained at σ = 0.02 millimeters. You test if the true mean diameter is significantly lesser than 8.25 millimeters. The P value of the test should be:

8. You need to test: H 0 ; μ = 25 v s H 1 ; μ > 25 . The P value of the test was found to be 0.094. A possible upper 95% confidence interval for μ is:

9. You need to test   H 0 ; μ = 50 v s H 1 ; μ > 50.   The Z test statistic is found to be 2.03. The P value of the test should be:

Answer 1