Analyze each of the situations described below. Do NOT do these problems! For ea

Question

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

a) 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?

b) 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.

c) 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?

d) 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.

Explanation / Answer

a.)   1-proportion Z-test

Reason Because here we have to compare sample proportion (74 out of 120 i.e 74/120) to the given hypothesized population proportion (3 or 2). And so 1-proportion Z-test can be used for the purpose.

b.)   1-sample t-test  and 95% confidence interval for mean

   Reason Because here we are concerned with the average time taken for 24 surgeries i.e mean of time and there is only one sample i.e 24 observations. So we use 1-sample t-test

c.)   Matched-pair t-test

Reason Because the farmer records two observation for the yield of 10 fields, one before adding fertilizers and one after. So basically there is a pair of before and after observation for each of the 10 fields. So we use matched-pair t-test.

d.)   2-sample t-test and 90% confidence interval for difference of means.

Reason Because in this question the law students randomly selects 20 cases of each type i.e there are independent pairs whose difference of means we have to compare and later find 90% confidence interval for difference of means.

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