# Important information about Normal Probability & Hypothesis Testing

Please use Excel and explain which test you use for problem 2 and 3 (t test, Anova, two tail or one tail...etc)

1.

a. The score on the entrance exam at a well-known, exclusive law school are normally distributed with a mean score of 200 and a standard deviation equal to 50. At what value should the lowest passing score be set if the school wishes only 2.5 percent of those taking the test to pass?

b. A machine is used to cut a metal automobile part to its desired length. The machine can be set so that the mean lengths of the part will be any value that is desired. The standard deviation of the lengths always runs at .02 inches. Where should the mean be set if want only .4 percent of the parts cut by the machine to be shorter than 15 inches long?

2.

Independent random samples were taken from normal distributions of the yearly production of ships built by the International Ship Building Company under (1) a fixed-position layout and (2) a project layout. The results are given in the accompanying table. Test the null hypothesis that the mean for the fixed-position layout is equal to that for the project layout. Use .05 for the level of significance.

Fixed-position layout 8 0 1 5 1 5 1

Project layout 6 1 1 1 4 4 4

3.

The accompanying table shows the grades for three randomly selected samples of students in economics, statistics, and accounting classes. Test the hypothesis that the mean grades are the same for all three classes. Use .05 for the level of significance.

Economics(X1) Statistics(X2) Accounting(X3)

80 100 95

90 90 90

70 90 88

100 75 82

60 95 85

100 60

80

60

#### Solution Summary

The solution provides step by step method for the calculation of normal probability, testing of hypothesis and ANOVA. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.