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The  ∑  symbol in a statistical equation indicates that we are to perform which arithmetic operation?

Frame score in beef cattle is based on height at the hips and is used as a measure of skeletal size.  Frame scores range from 1 to 10 with a higher number indicating a taller animal.  Independent random samples of frame scores were selected from the Angus and Simmental breeds of beef cattle with the following results: Angus Simmental 5 7 6 7 7 8 5 6 7 7 6   Using the appropriate table, find the critical F value needed to test the null hypothesis that the breed means for frame score are equal (use α = 0.05).

A crop scientist would like to know the average yield of soybeans in Ohio (in bushels per acre).  A random sample of 225 soybean fields in Ohio yields a mean of 48 bushels per acre and a standard deviation of 7.5 bushels per acre. Estimate the population mean for the yield of soybeans In Ohio using a 95% confidence interval.

The weights in pounds of 23 dogs were used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf:. Stem     Leaves                                                    3            2     4 4            0     3     4     5     7     8     9 5            0     1     2     3     4     5 6            1     2     5     6     7 7            0     1 8 9            8 Use the stem-and-leaf display to find the lower quartile, median, and upper quartile and then use these values to construct a box plot.  Use the box plot to identify any suspect or highly suspect outliers in this dataset.

Toyota would like to know how many miles per gallon the average person gets when driving the hybrid Toyota Prius.  A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg.  The point estimate of the population mean for the miles per gallon of the Toyota Prius would be:

The following table shows litter sizes for sows in four breeds of pigs. Yorkshire     Landrace     Hampshire     Duroc      8                   9                   8                 7     10                  9                   7                 8     11                10                   8                 9     11                10                   9                 7       9                  8                                                 49                46                 32               31 – treatment totals     9.8               9.2               8.0              7.5 – sample means     The total sums of squares in the Analysis of Variance table for this problem is equal to ____________.                                                                                    

The heights in inches of young growing trees were measured at a nursery and used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf: Stem                       Leaves                                     3               2     4 4               0     3     4     5     7     8     9 5               0     1     2     3     4     5 6               1     2     5     6     7 7               0     1 8 9               8 Based on the stem-and-leaf display, the lower quartile for this set of tree heights is __________ inches.

Toyota would like to know how many miles per gallon the average person gets when driving the hybrid Toyota Prius.  A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg.  Find the 90% confidence interval for the population mean for the miles per gallon of the Toyota Prius.

An animal scientist wants to determine the degree of association between carcass quality grade (variable X) and selling price per pound of carcass (variable Y).  The data for a random sample of 10 Angus steer carcasses are shown in the following table. Quality grade, X Carcass price per pound, Y 5 $1.09 7 1.19 4 0.99 5 1.04 8 1.21 6 1.18 4 0.94 7 1.15 8 1.23 6 1.12 The animal scientist performs a hypothesis test using a significance level of 0.05 to determine if the correlation between carcass quality grade and carcass price per pound is greater than zero. Ho:  

Assume that 20% of all pigs die between birth and weaning.  In a random sample of 200 births, let X be the number of pigs that die between birth and weaning.  Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 200 that die between birth and weaning is greater than or equal to 50.