Statistics Procedures

Analyze each of the situations described below. Do NOT do these problems! For each, indicate which procedure you would use and explain why you chose that procedure. You only get 5 of the 10 points if your initial post doesn’t include explanations! A procedure may be used more than once. The different procedures are: 1-proportion z-test, 2-proportion z-test, 1-sample t-test, 2-sample t-test (difference of means), and a matched or blocked pairs t-test (mean of differences), or the confidence intervals that go along with any of those tests. It may be helpful to watch this short video first: https://spark.adobe.com/video/Ei8lgd1KdZk29. There is no follow-up question this week. I want you to discuss the question with one another to arrive at the 4-correct solutions as a class. One of you will have to take the lead!

A union organization would like to represent the employees at the local market. A sample of the employees revealed 74 of 120 were in favor of the union. Does the union have required 3 to 2 majority?
An oral surgeon is interested in estimating how long it takes to extract all four wisdom teeth. The doctor records the times for 24 randomly chosen surgeries. Estimate the time it takes to perform the surgery with a 95% confidence interval.
A farmer would like to know if a new fertilizer increases his crop yield. In an effort to decide this, the farmer recorded the yield for 10 different fields prior to adding fertilizer and after adding the fertilizer. The farmer assumes the crop yields are approximately normal. Does the fertilizer work as advertised?
In a study to determine whether there is a difference between the average jail time convicted bank robbers and car thieves are sentenced to, the law students randomly selected 20 cases of each type that resulted in jail sentences during the previous year. A 90% confidence interval was created from the results.

Solution Preview

A union organization would like to represent the employees at the local market. A sample of the employees revealed 74 of 120 were in favor of the union. Does the union have required 3 to 2 majority?

For this kind of problem, we will use a 1-proportion z-test. This is because we are testing the null hypothesis of proportion that (74/120) is equal to 3 to 2 majority (only one single proportion, i.e., we are testing for just one proportion). If we end up rejecting the null hypothesis (this is to mean accepting the alternative hypothesis that 74/120 is not equal to 3 to 2 majority),

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