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Case Study Scenario: A 27-year-old male presents to the emergency room with confusion, difficulty speaking, shortness of breath, cough, fatigue, and diaphoresis. His respiratory rate is 44 breaths per minute, and his oxygen saturation is 84%. The patient has a 10-year history of asthma and typically uses a salbutamol inhaler (2 puffs, three times a day) and salmeterol (2 puffs every morning). He is an active basketball player but often forgets to take his inhalers as prescribed. He has a history of chain smoking for about 10 years, which he quit recently after his girlfriend left him, and has been smoke-free for some time. He received a flu vaccination six months ago and has a family history of chronic obstructive pulmonary disease (COPD). His mother is an active smoker, although they do not live together. Which of the following problems is the client mostly experiencing?

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.  A randomized block design is used to compare the frame scores of Angus and Simmental calves where the blocks consist of calves of similar ages.  Three blocks are used, where block 1 contains calves that are 320 to 340 days of age, block 2 contains calves that are 341 to 360 days of age, and block 3 contains calves that are 361 to 380 days of age.  The frame scores are as follows:   Angus Simmental Block totals Block 1 5 6 11 Block 2 6 7 13 Block 3 7 8 15 Breed totals 18 21 39 The partially completed ANOVA table for this experiment is as follows: Source   df     SS     MS      F  Total   5.500     Breed   0.167 0.167 0.25 Block   4.000 2.000   Error   1.333 0.667   Calculate the F statistic for blocks.

We want to test the following null and alternative hypotheses about a population proportion: Ho:  p = 0.20 Ha:  p ≠ 0.20 We observe 300 successes in a sample of 1,000 observations.  Assume that it is valid to use large-sample procedures in this problem. Calculate the test statistic needed to test the null hypothesis.  Should we reject or not reject the Ho?  Explain.  Use a significance level of α = 0.05.

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 error.

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   In the Analysis of Variance table, the degrees of freedom for total, breeds, and error, respectively, are:

A ________ ________ error occurs if we fail to reject a null hypothesis when it is false.

A college professor wants to estimate the difference in mean test scores of students who have taken his statistics and genetics classes in the past 10 years.  He selects a random sample of 20 student records from the statistics course and a random sample of 22 student records from the genetics course.  These two samples were independent random samples.  The study provided the results shown in the table below.  Construct a 95% confidence interval for the true difference in population means of these two populations of students.   Statistics Genetics Sample size 20 22 Sample mean 78 75 Sample standard dev. 10 12

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.  Should the scientists reject or not reject the null hypothesis?  Explain.

A local consumer reporter wants to compare the average cost of grocery items purchased at 3 different supermarkets:  Kroger, Giant Eagle, and Sam’s Club.  Prices (in dollars) were recorded for a sample of 10 randomly selected grocery items at each of the 3 supermarkets (i.e., a total of 10 x 3 = 30 prices were recorded).  We will consider this to be a one-way analysis of variance (i.e., a completely randomized design).  The partially completed Analysis of Variance table is shown below: Source               df          SS          MS          F        Total                               120 Supermarkets                  20 Error                               100                                          State the null and alternative hypothesis being tested by the consumer reporter..

In the 1970’s it was generally assumed that the mean birth weight of Angus beef cattle was 75 lb.  A researcher believes that, due to selection for increased size and growth rate in Angus, the average birth weight is now greater than 75 lb.  He obtains a random sample of n = 144 birth weights of Angus calves and calculates a sample mean of 85 lb and a sample standard deviation of 10 lb. Calculate the test statistic needed to test the null hypothesis.