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.

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Definitions:

Cohesive Group

A collective of individuals who are united in their goals, values, or interests, displaying strong bonds and a high level of mutual support.

Group Attractiveness

The degree to which a group is considered appealing or desirable to its current or potential members, influenced by factors like cohesion, identity, and perceived benefits.

Group Cohesiveness

The extent to which members of a group support and validate one another while working towards a common goal.

Informal Leadership

The ability to influence and guide others without having a formal authority or position, often resulting from personal traits, expertise, or relationships.