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                      Applied Statistics Exam                                    

(2 Hours)

Question 1:

1) The following is the frequency distribution of the weekly wages for 100 labors in the weaving and spinning industry:

   a) Calculate the arithmetic mean x mean, the median, and the mode and illustrate their position graphically.

   b) Plot an ogive for the weekly wages.

2) The following are the first four moments about Zero for a certain distribution:

      µ1 = 1,        µ2 = 4.8,        µ3 = 12.4     and      µ4 = 67.12   

 Calculate the Coefficient of skewness   α1, and the Coefficient of kurtosis  α2.

Question 2:

1) A random sample of 100 soldiers is selected without replacement from a population of size 900 men.  The mean height of the population is 71 inches, with a standard deviation 2.5 inches. Determine the probabilities for the following sample heights:

   a) between 71 and 71.4 inches

   b) greater than 71.6 inches 

   c) less than 70.5 inches

2) A researcher wishes to determine which of the two types of fuel provides more miles per gallon. Two independent random samples of size 15 cars were selected, and each car was driven 2,000 miles by employees on normal business. A different type of fuel was used in each sample. The following results were obtained:

   a) Construct a 95% Confidence interval estimate of the difference between mean fuel consumption.

   b) Should a null hypothesis that there is no difference between the fuel be accepted.

Question 3:

1) An experimenter investigated the impact of temperature  settings on the yield of a chemical process. He used four different settings for samples of five production run each.  He computed the following valued:

                               SSTR = 390 ,    SSE = 120

   a) Construct the ANOVA table.

   b) Should the experimenter accept or reject the null hypothesis of identical mean yields?

2) The following data represents disposal income end personal consumption expenditure for the United States during the five -year period from 1964 through 1968:

   1- Using the method least squares, determine the estimated linear regression equation that provides consumption expenditure predictions for specified levels of disposal income.

   2- Calculate the coefficient of determination  r² and interpret it.

   3- Test the significance of the true regression coefficient β .

Note that:

              t (28,   0.025) = 2,048             t (3,   0.025) = 3.182

              F (3.16,  0.05) = 3.24

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