All calculations should be completed only using R or RStudio. For each part, include a copy of your R code used and the output of your code. (i.e. Copy and paste the relevant pieces into a Word document (or other word processing document).)

Submission: Since you will need to copy your R code and the code output, the best way to complete assignment is by using a word processor such as MS Word or Open Office Document. (I have a link posted on our Brightspace page in the ``Useful Links'' module where you can download Microsoft 365 for free.)

Part 2 (5 points)

Include any used R code and the written up solutions to all parts below.

From a random sample of 549 items made by a particular manufacturing process, it is found that 24 are defective.

(a) Suppose we want to test the research hypothesis that to proportion of defective items is greater than 3%. Copy and paste the appropriate R command and output you would use to do test.

(b) Clearly state the p-value you found from part (a). Using the significance level =0.05, should we reject the null hypothesis?

(c) Write sentence stating your conclusion of the hypothesis test you just performed. (i.e. Write conclusion in plain language so that a non-statistician could understand the conclusion of the test.)

(d) Suppose that in another manufacturing centre in 793 items made by the same manufacturing process as above, it is found that 61 items are defective. Calculate a 95% confidence interval (i.e. a two-sided confidence interval) for the true proportion of defective items manufactured at this plant. Copy and paste the appropriate R command and output you would use to do the question. In an additional line, clearly state the values you get for the confidence interval from your output.

(e) According to your confidence interval in part (d), is it reasonable to conclude that 10% of the items created at this plant are defective? Explain, using your confidence interval.