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Scientists are interested in determining if the mean alkalinity level of water specimens from the Han River in Seoul, Korea is greater than 50 milligrams per liter (mpl).  They select a random sample of 100 water specimens from the river and find a sample mean of 70 mpl and a sample standard deviation of 15 mpl.  They decide to test the hypothesis that the population mean for alkalinity level of water in the Han River exceeds 50 mpl using a significance level of 0.01.  Find the value of the test statistic used to test this hypothesis.

It is desired to estimate the proportion of cows conceiving at first service (breeding) in an artificial insemination (AI) program used on a particular farm.  A random sample of 50 cow records is chosen; 30 of these 50 cows conceived at first service.  Construct a 95% confidence interval for the true population proportion of cows conceiving at first service on this farm.  You can assume that large-sample procedures are appropriate.

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a school levy in a certain school district.  A random sample of 400 people of voting age is selected.  Results of the poll show that 240 of the 400 people polled plan to vote in favor of the school levy.  Construct a 99% confidence interval for the true population proportion of people who plan to vote in favor of the school levy.

Find the probability of an observation lying more than z = 1.77 standard deviations above the mean.

The owner of a herd of cows wants to determine the influence of the ages of his cows on the amount of calving difficulty that occurs in his herd.  He constructs the following table:                             Age of Cow (in years)                                           0-2     3-5     6-10     over 10   Total No difficulty     40      35       20          5            100 Difficult birth   35      45       15          5            100 Total                  75      80       35        10           200   Given that the randomly selected cow had no difficulty in giving birth to her calf, what is the probability that she was more than than 2 yr old?

The weights (in pounds) of a sample of 6 dogs are as follows: Dog Weight 1 30 2 32 3 26 4 42 5 40 6 46 Find the mean of the weights of this sample of 6 dogs.

A box plot can be used to detect outliers in a dataset.  Assume that we have derived the following values for a dataset: lower outer fence = 169 lb       lower inner fence = 197.5 lb lower quartile = 226 lb             upper quartile = 245 lb upper inner fence = 273.5 lb   upper outer fence = 302 lb   The two lightest weights in the dataset are 160 lb and 165 lb.  The two heaviest weights in the dataset are 280 lb and 285 lb.  Based on a box plot, which one of the following statements is correct?

Which one of the following is not an assumption for the randomized block design?

A severe drought has affected several western states in recent years.  A Christmas tree farmer is worried about the drought’s effect on the size of his trees.  To determine whether the growth of his trees has been reduced by the drought, the farmer decides to take a sample of the heights of 6 trees and obtains the following results (recorded in inches): Tree Height 1 60 2 57 3 62 4 69 5 46 6 54 Find the variance of the heights of this sample of 6 trees.

Finnish Landrace ewes are noted for producing “litters” of lambs. The number of lambs in a litter for a sample of 6 Finnish Landrace ewes is as follows:  Ewe Number           Number of Lambs in Litter        1                                        3        2                                        4        3                                        3        4                                        2        5                                        5        6                                        4   Calculate the standard deviation of litter size.