Find the probability of an observation lying more than z = 1.95 standard deviations above the mean.

A professor in the Department of Animal Sciences wants to estimate the mean weight of the Suffolk breed of lambs shown at the Ohio State Fair in the past five years.  Therefore, he selects a random sample of n = 25 lamb weights and obtains a sample mean of 125 lb and a sample standard deviation of 15 lb.  Construct a 95% confidence interval for the true population mean of the weights of Suffolk lambs shown at the Ohio State Fair in the past five years.

Independent random samples of litter sizes were selected from the Yorkshire and Landrace breeds of swine with the following results: Yorkshire          Landrace 8 pigs                    7 pigs 9                            8 10                          9 8                            8 9                            7 10                               54                        39  The correction factor (correction for the mean) in this problem is 786.27272. Calculate the Total Sums of Squares.

You are interested in purchasing a new car.  One of the many points you wish to consider is the resale value of the car after 5 years of ownership.  Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 90% confidence interval.  You manage to obtain data on 16 recently resold 5-year-old foreign sedans of that model.  These 16 cars were resold at an average price of $10,000 with a standard deviation of $1,500. Estimate the true mean resale value of this model of foreign car using a 90% confidence interval.

A plant breeder develops a new wheat variety she hopes will yield more in the plains than the three most popular varieties under dry-land farming conditions.  She sets up a randomized block experiment with the three major types of soil in the region – sand, clay, and loam – as the blocks.  She selects a field with each soil type, divides it into four sections, and randomly selects one of the four wheat varieties for planting in each section.  The yields in bushels per acre in each section are shown in the following table. Variety Block A B C D Total Sand 20 21 21 18 80 Clay 25 24 21 20 90 Loam 30 28 22 20 100 Total 75 73 64 58 270 The correction factor for this Analysis of Variance is 6,075 and the total sums of squares is 141. What is the correct conclusion regarding varieties (i.e., treatments) in this randomized block experiment?

Assume that you own a herd of Bison.  By plotting the birth weights of the calves born in your herd in the spring calving season, you determine that the distribution of birth weights was symmetric and mound-shaped with a mean of 80 lb and a standard deviation of 10 lb.  You would expect that approximately 95% of the calves born in your herd during the spring calving season would have birth weights between __________ and __________ lb.

The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68     73     66     76     86     74     61     89     65     90 69     92     76     62     81     63     68     81     70     73     60     87     75     64     82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf.  Based on the stem-and-leaf display, the lower quartile for this set of weights is __________ lb.

A vet clinic has found that the number of patients per day has an average of 100 and a standard deviation of 10.  If the distribution of number of patients seen per day is symmetric and mound-shaped, what percentage of the days would be expected to have between 80 and 120 patients?

A farm supply store manager wants to predict monthly sales, Y, for her company using advertising expenditures, X.  She has collected 10 months of data on past performance as shown in the following table. Advertising expenditures, in thousands of dollars, X Monthly sales, Y XY X2 Y2 1.2 101 121.2 1.44 10,201 0.8 92 73.6 0.64 8,464 1.0 110 110.0 1.00 12,100 1.3 120 156.0 1.69 14,400 0.7 90 63.0 0.49 8,100 0.8 82 65.6 0.64 6,724 1.0 93 93.0 1.00 8,649 0.6 75 45.0 0.36 5,625 0.9 91 81.9 0.81 8,281 1.1 105 115.5 1.21 11,025 TOTAL 9.4 959 924.8 9.28 93,569 Calculate the slope of the regression line for the regression of Y on X.

An egg wholesaler wants to compare four methods of shipping eggs to determine which method results in the fewest broken eggs.  Five lots of eggs are shipped using each of the four methods.  The number of broken eggs in each lot is recorded and shown in the table below.  The wholesaler wants to determine if the average number of broken eggs is the same for each shipping method.  Therefore, he tests the null hypotheses using a 0.01 significance level. Shipping Method Sample lot no. A B C D 1 4 9 1 9 2 3 7 6 7 3 1 6 4 7 4 2 8 3 6 5 5 8 4 8 Total 15 38 18 37 Mean 3.0 7.6 3.6 7.4 What is the degrees of freedom for total, treatment, and error in the Analysis of Variance table?