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. 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, and a matched or blocked pairs t-test (or interval for any of these).

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. one proportion z-test.

To test the population propotion equal to certian value one propotion z-test is used.

In this, to test whether the population is having 3 to 2 majority i.e to test whether the population proportion = 2/3 or not by using the one propotion test.

b. 1-sample t-test.

1-sample t-test is used to test whether the population mean is equal to a certian value or to find the confidence interval for population mean.

In this case to estimate the 95% confidence limit for mean time to extraction all four wisdom tooth,. One sample and 95 % confidence interval for mean time of extraction of ll four wisdom tooth. so 1-sample t-test is being used.

c.matched pairs t-test.

Here to test the effectiveness of the fretilizer on the crop yield. Here the same(sample) 10 fields are used to collect data on the yield prior to and after adding the fertilizer. Hence pairs t-test is used to test whether average differience in yield prior to and after adding the fertilizer is significant.

d.2 sample t-test. 90% confidence interval for difference between the mean(average) jail time of convicted bank robbers and cr thieves. Here we have two different samples one each for bank robbers and car thieves. Hence two sample t-test.

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