The Reliability of Two Types of Machines Used in the Same

question 96

Essay

The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials.
a.Give a point estimate for the difference between the population proportions of these machines.
b.Calculate the pooled estimate of the population proportion.
c.Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a .10 level of significance.

---

Definitions:

Regression

A statistical method used to determine the relationship between a dependent variable and one or more independent variables.

Variance

Average squared deviation from the mean.

Degrees Freedom

Degrees of freedom refer to the number of independent values or quantities which can be assigned to a statistical distribution or to the number of variables minus the number of constraints in a system.

F-ratio Equation

A statistic used in ANOVA tests, calculated as the variance between group means divided by the variance within the groups.