Blog

A randomized block design is used to compare postweaning average daily gains of 4 breeds of beef cattle, Hereford, Angus, Charolais, and Simmental (we can think of the breeds at the “treatments”).  The breeds are divided into 3 weight classes (i.e., 3 blocks).  Block 1 contains cattle weighing 450 to 500 lb at the beginning of the experiment, block 2 contains cattle weighing 500 to 550 lb at the beginning of the experiment, and block 3 contains cattle weighing 550 to 600 lb at the beginning of the experiment.  The postweaning average daily gains (in pounds per day) are as follows:  Block Hereford Angus Charolais Simmental 1 3.50 3.60 3.70 3.75 2 3.55 3.63 3.71 3.80 3 3.56 3.62 3.80 3.90 The partially completed ANOVA table for this experiment is as follows: Source df SS MS F Total   .160     Breed   .139 .046 46 Block   .014 .007   Error   .007 .001   Calculate the F statistic for blocks. Do the block means differ (i.e., was blocking effective in removing variation in average daily gain)?  Use a significance level of α = 0.05.

A study was conducted to determine whether a student’s final grade in a high school math class is linearly related to his or her performance on the math ability test administered before college entrance.  The math test scores and final grades for a random sample of 10 students are shown below. Final Grade in Math Class (X)          Math Ability Test Score (Y) 65                                                             39 78                                                             43 52                                                             21 82                                                             64 92                                                             57 89                                                             47 73                                                             28 98                                                             75 56                                                             34 75                                                             52   What are the correct null and alternative hypotheses if we want to test that the correlation between these two variables is significantly different from zero (i.e., we want to perform a two-sided hypothesis test)?

A large labor union wishes to estimate the mean number of hours per month that union members are absent from work.  The union samples 475 of its members at random and monitors their working time for 1 month.  At the end of the month, the total number of hours absent from work is recorded for each employee.  The mean and standard deviation of the sample are 9.6 hours and 3.6 hours, respectively.  Find the 95% confidence interval that can be used to estimate the mean (μ) of the entire population of number of hours absent from work per month.

For most populations, sample sizes of n > ________ will be adequate for the sampling distribution of the sample means to be normally distributed.

Find the probability of an observation lying more than z = 0.58 standard deviations below the mean.

Assume that we have a herd of 50 horses and that we want to select a random sample of 5 of the horses for an experiment.  We begin at row 5 column 1 of a random number table and observe the random numbers shown in the table below.         Col.           1 2 3 4 5 6 Row 5: 37570 39975 81837 16656 06121 91782   6: 77921 06907 11008 42751 27756 53498 Which one of the following is the correct set of 5 randomly selected horses to include in our experiment, assuming that we go from left to right across the rows of random numbers?

A bottling company needs to produce bottles that will hold 12 ounces of liquid for a local beer maker.  Periodically, the company receives complaints that their bottles are not holding enough liquid.  To test this claim, the bottling company randomly samples 15 bottles and finds the average amount of liquid held by the 15 bottles is 11.90 ounces and the standard deviation is 0.20 ounces. Which one of the following is the set of hypotheses the company wishes to test?

The Australian Journal of Zoology reported on a study of the diets and water requirements of spinifex pigeons.  Sixteen pigeons were captured in the desert and the crop (i.e., stomach) contents of each were examined.  The weight of dry seeds in the crop of each pigeon was measured and recorded.  The mean was 1.4 grams and the standard deviation was 0.20 grams. Find a 99% confidence interval for the average weight of dry seeds in the crops of spinifex pigeons inhabiting the Western Australian desert.

An industrial psychologist is investigating the effects of work environment on employee attitudes.  A group of 20 recently hired sales trainees were randomly assigned to one of 4 different “home rooms” with 5 trainees per room.  Each room was identical except for the color of the walls.  The 4 colors used were light green, light blue, gray, and red.  Therefore, in this experiment the 4 treatments were the 4 room colors.  The psychologist wants to compare the mean attitudes of the trainees assigned to the 4 rooms with different colors.  At the end of the training program, the attitude of each trainee was measured on a 60 point scale (the lower the score, the poorer the attitude).  The data were subjected to an analysis of variance.  The partially completed Analysis of Variance (ANOVA) table was as follows: Source           df       SS              MS              F     Total                       1,829.75 Treatments             1,678.15 Error                          151.60                                      Find the Mean Squares for treatments.

The following is a valid probability distribution for a discrete random variable, X: X             4           9            20          P (X)     -0.30      1.0         0.30