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The average breaking force of a certain type of fiber must be greater than 200 pounds...

The average breaking force of a certain type of fiber must be greater than 200 pounds per square inches (lppc). Previous experiments have shown that we can assume that the breaking force is normally distributed with a standard deviation σ = 4.5 lppc. A sample of 8 fibers gave the following breaking forces (in lppc): 210, 206, 198, 202, 201, 198, 199, 205.

(a) Formulate a null hypothesis against alternative hypothesis to verify that this type of fiber is acceptable.

(b) Calculate the observed value of the test statistic to test the hypotheses of part (a).

(c) Based on the value of the test statistic in part (a): (i) give the conclusion to α = 5%; (ii) give the conclusion to α = 10%.

(d) Suppose that a sample of 30 fibers gives an average breaking force of ¯x = 202, 375 CFPA. For this new study, calculate the observed value of the test statistic for test the hypotheses in part (a) and give the conclusion to α = 5%.

math   Statistics-And-Probability   
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