hypothesis testing

Question

Because of high production change-over time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of £320 per hour. A sample of 1,000 products have been analysed using the innovative manufacturing method. The director of manufacturing observed the mean cost was £300 per hour and a standard deviation of £20 per hour.

Define an appropriate system of hypotheses (null hypothesis and alternative hypothesis) to test whether the mean cost of production is reduced.]

What assumption(s) about the population is/are necessary to perform this test?

What is the value of the test statistic?

What is the approximate p-value associated to the test statistic?

What is the critical value?

At the 1% significance level, what is your conclusion? If the level of significance was 5% would your conclusion be different? Explain your answer.

Calculate the 95% approximate confidence interval for the population mean cost of production.

Answer 1

Hello Jamahl,

You should send in some work for us to help you with. Also, you need to tell us how you do computations in your statistics class (tables, statistical calculator, or computer software).

I will get you started. You first need to write the null and alternative hypotheses.

The null hypothesis is what you expect the mean to be if nothing changes (null means nothing).

The null hypothesis always has an equal sign.

It is about a population mean so it will have a mu.

H₀: μ = ____. See if you can fill in the blank.

The alternative hypothesis has two different forms, and I don't know which one your school uses. At my school, we always use <, >, or ≠ in the alternative hypothesis. It will look like

H_a: μ ______ _______. Pick the correct inequality symbol and use the same number in the blank as in H₀.

(<, >, ≠) (number)

The main assumption you should mention is that the sample should be random. Notice that the problem says "sample" not "random sample". Usually the problem will say "random sample".

The method for all the computations will depend on how you do them in your class (table, stat. calculator, or computer). You would have to tell about that when you send in a question.