Data set 2 presents a sample of the number of defective flas

Data set 2 presents a sample of the number of defective flash drives produced by a small manufacturing company over the last 30 weeks. The company’s operations manager believes that the number of defects produced by the process is less than seven defective flash drives per week. Use this online calculator (or any statistical package that you are comfortable with) to construct a hypothesis test to verify the operations manager’s claim. Your hypothesis test should include null and alternative hypotheses, a t test statistic value, a p value, a decision, and a conclusion.

6

Please illustrate in detail the hypothesis and its conclusions.

Solution

Given data is about number of defective items per week for 30 weeks and based on the same the average is calculated as given in the following table.

The company’s operations manager believes that the number of defects produced by the process is less than seven defective flash drives per week. As per the above calculations the average number of defects is more than seven, therefore the Null Hypothesis may be that average number of defectives is seven (>=7) as against the alternative hypothesis of manager that number of defects is less than seven.

The t-statistic is defined as:

t = ((Sample mean - Population mean)/ S) * SQRT(n) where S is standard deviation estimator based on sample values with denominator (n-1) in place of n in the formula for standard deviation.

The calculated value of t is very much lower than the tabulated values of t for any level of significance, therefore null hypothesis is accepted and tha claim of manager is rejected.