The grades of 8 students on an exam were as follows: Student Grade 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79     Find the standard deviation of the grades of these 8 students.

Find the probability of an observation lying more than z = 1.56 standard deviations below the mean.

If the variation between sample means is large relative to the variation within the samples, it indicates that there is a real difference between the population means.

A 2 x 4 factorial experiment is conducted to compare yields of 4 varieties of soybeans that are planted in rows either 15 inches or 30 inches apart.  Two plots of ground are randomly assigned to each combination of soybean variety and row spacing.  The yields of soybeans (in bushels per acre) are as follows:           Rows 1 2 3 4 15″ 45 46 47 46   46 46 48 43 30″ 35 41 42 39   32 39 38 41 The partially completed ANOVA table is as follows: Source df SS MS F Total   319.75     Variety   41.25 13.75 5.0 Row spacing   225 225 81.8 Variety x row spacing   31.5     Error   22 2.75   Should we reject or not reject the null hypothesis for the interaction between variety and row spacing?  Use a significance level of α = 0.05.

A two-factor factorial experiment is conducted to compare litter sizes of Yorkshire and Landrace sows derived either from a line unselected for litter size or from a line that has gone through 15 years of selection for increased litter size.  Two sows of each breed are randomly selected from each line.  Their litter sizes are as follows:                                   Yorkshire       Landrace            Unselected line               8                     9                                        9                    10 Selected line                 11                    11                                      10                      9                                                                                     The partially completed ANOVA table is as follows:  Source             df             SS                MS            F  Total                              7.875 Line                               3.125            3.125       3.57 Breed Line x Breed Error                              3.500            0.875                                                                                       Calculate the sums of squares for breed.

We want to test the hypothesis that the mean weight of a breed of dogs is greater than 40 lb.  Therefore, we obtain the weights of a random sample of 36 dogs. The dogs in the sample weighed an average of 43 lb with a standard deviation of 6 lb.  We want to test:    Ho:  μ = 40 lb    Ha:  μ > 40 lb using a significance level (α) = 0.05. Should we reject Ho:  μ = 40 lb?  Explain.

Health care issues are receiving a greal deal of attention in both the academic and political arenas.  A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance.  The ages (in years) of 9 uninsured senior citizens were as follows: Senior Citizen Age 1 65 2 70 3 64 4 84 5 74 6 72 7 87 8 79 9 80 Calculate the mean age of these 9 senior citizens.

The average height cows of a certain breed is 54 inches and the standard deviation of the heights is 8 inches.  Fifteen percent of the cows are expected to be less than X inches tall.  Find the value of X.

We are interested in comparing the mean supermarket prices of two leading colas in the Columbus area.  Assume that we have independent random samples of prices of six-packs at 8 supermarkets.  The data are shown in the following table: Supermarket      Brand 1       Brand 2  1                             $2.25          $2.30 2                               2.47            2.45 3                               2.38            2.44 4                               2.27            2.29 5                               2.15            2.25 6                               2.25            2.25 7                               2.36            2.42 8                               2.37            2.40 _______________________________________ Mean                       $2.3125       $2.3500 Standard deviation  $0.1007       $0.0859 _______________________________________ Find the point estimate for the difference in mean price of Brand 1 and Brand 2, assuming that these are independent random samples.

A swine producer reads a report stating that the average litter size in the US is 7.8 pigs per litter.  However, he feels that the average litter size on his farm is not 7.8 pigs/litter (he wants to detect departure in either direction from the hypothesized mean of 7.8 pigs/litter).  To test his hypothesis, he reviews his records for the past year and randomly selects 16 litters, which averaged 8.0 pigs/litter.  The standard deviation is 1 pig/litter. Does the sample obtained by the producer provide sufficient evidence to reject the null hypothesis?  Explain.