For a physiology class experiment, a student is fitted with a lightweight waterproof device that measures her average pulse rate over 2-hourly intervals. Consider 12 consecutive intervals over a 24-hour period, and let X be the number of these intervals in which the average pulse rate is less than 100 beats per minute. Is it reasonable to treat X as an observation from a binomial distribution? Justify your answer.

Below is the data of a factorial experiment consisting of 2 levels of factor A, ie levels 1 and 2, and 3 levels of factor B, ie levels 1, 2, and 3.

                                                                                                Factor B

                                                                Level 1                  Level 2                  Level 3

                                Level 1                  135                         90                           75

Factor A                                               165                         66                           93

                                Level 2                  125                         127                         120

                                                                95                           105                         136

Create an ANOVA table! And what can you conclude? α = 0.05

(Use manual calculations and Minitab software)

An experiment was conducted to study responses to different methods of taking insulin in patients with type I diabetes. The percentages of glycosolated hemoglobin initially and 3 months after taking insulin by nasal spray are given in the table below.

Patient Number            Before          3 Months After

1                                     12                      10.2           

2                                   7.7                       7.9

3                                     5.9                       6.6

4                                    9.5                     10.4

5                                    7.6                      8.8

6                                     8.6                      9

7                                     11                       9.5

8                                    6.9                     7.7

Conduct a two-sided Wilcoxon Sign Rank Test with alpha = 5% to determine if there is a significant difference in glycosolated hemoglobin after taking insulin by nasal spray. Note: Conduct your subtraction by Before – 3 Months After

38. True or False: There is no significant difference in glycosolated hemoglobin in patients 3 months after taking insulin by nasal spray.

An experiment is planned to compare three treatments applied to shirts in a test of durable press fabric treatments to produce wrinkle-free fabrics. In the past formaldehyde had been used to produce wrinkle-free fabric, but it was considered an undesirable chemical treatment. This study is to consider three alternative chemicals: (a) PCA (1-2-3 propane tricarbolic acid), (b) BTCA tetracarboxilic acid), and (c) CA (citric acid). Four shirts will be used for each of the treatments. First, the treatments are applied to the shirts, which are then subjected to simulated wear and washing in a simulation machine. The chemical treatments will not contaminate one another if they are all placed in the same washing machine during the test. The machine can hold one to four shirts in a single simulation run. At the end of the simulation run each of the shirts is measured for tear and breaking strength of the fabric and how wrinkle-free they are after being subjected to the simulated wear and washing. The comparisons among the treatments can be affected by (a) the natural variation from shirt to shirt; (b) measurement errors; (c) variation in the application of the durable press treatment; and (d) variation in the run of the simulation of wear and washing by the simulation machine. Following is a brief description of three proposed methods of conducting this simple experiment.

Method I. The shirts are divided randomly into three groups of four shirts. Each group receives a durable press treatment as one batch and then each batch is processed in one run of the simulation machine. Each run of the simulation machine has four shirts that have receive and same treatment. There are three runs of the simulation machine.

Method II. The shirts are divided randomly into three treatment groups of four shirt each, and the durable press treatments are applied independently to single shirts. The shirts are grouped into four sets of three, one shirt from each durable press treatment in each of the four sets, and each set of three so constructed is used in one run of the simulation machine. There are four runs of the simulation machine.

Method III. The shirts are divided randomly into three groups of four shirts. The durable press treatments are applied independently to single shirts. The simulation of wear and washing is done as in Method I.

a. Which method do you favor?

b. Why do you favor the method you have chosen?

c. Briefly, what are the disadvantages of the other two methods?

An experiment consists of tossing a single die and observing the number of dots that show on the upper face. Events A, B, and C are defined as follows.

Find the probabilities associated with the events below using either the simple event approach or the rules and definitions from this section. (Enter your probabilities as fractions.)

(a)    S


(b)    A|B


(c)    B


(d)    A ? B ? C


(e)    A ? B


(f)    A ? C


(g)    B ? C


(h)    A ? C


(i)    B ? C

to evaluate the effectiveness of a new type of plant food developed for tomatoes, an experiment was conducted in which a random sample of 42 seedlings was obtained from a large greenhouse having thousands of seedlings. Each of the 42 plants received 72 grams of this new type of plant food each week for 4 weeks. The number of tomatoes produced by each plant was recorded yielding the following results: X bar=31.35 s=3.865 (a) Assuming that the seedlings chosen are taken from a population which is normally distributed, determine a 95% confidence interval estimate for the average number of tomatoes that would have been produced by all the seedlings in the greenhouse if they have recieved 72 grams of thee new plant food, once a week for 4 weeks. Use three decimals. Lower Bound : Upper Bound : (b) The greenhouse is currently using a plant food called "Supr-Grow". The average number of tomatoes produced by seedlings in the greenhouse with "Supr-Grow" is 32. Based on the interval in (a), should the greenhouse switch to the new plant food? (YES or NO) (c) A researcher has started with a new sample and a given degree of confidence that the average number of tomatoes the seedlings produced on the new plant food is between "33.00628 and 35.89372". Suppose the sample size and standard deviation are the same as given above. What alpha did the researcher use in the construction of this statement? (Input your answer as a decimal)

to evaluate the effectiveness of a new type of plant food developed for tomatoes, an experiment was conducted in which a random sample of 42 seedlings was obtained from a large greenhouse having thousands of seedlings. Each of the 42 plants received 72 grams of this new type of plant food each week for 4 weeks. The number of tomatoes produced by each plant was recorded yielding the following results: X bar=31.35 s=3.865 (a) Assuming that the seedlings chosen are taken from a population which is normally distributed, determine a 95% confidence interval estimate for the average number of tomatoes that would have been produced by all the seedlings in the greenhouse if they have recieved 72 grams of thee new plant food, once a week for 4 weeks. Use three decimals. Lower Bound : Upper Bound : (b) The greenhouse is currently using a plant food called "Supr-Grow". The average number of tomatoes produced by seedlings in the greenhouse with "Supr-Grow" is 32. Based on the interval in (a), should the greenhouse switch to the new plant food? (YES or NO) (c) A researcher has started with a new sample and a given degree of confidence that the average number of tomatoes the seedlings produced on the new plant food is between "33.00628 and 35.89372". Suppose the sample size and standard deviation are the same as given above. What alpha did the researcher use in the construction of this statement? (Input your answer as a decimal)

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use alpha= .05 .

Complete the following ANOVA table (to 2 decimals, if necessary). Round your p-value to 4 decimal places.

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use  = .05.

1. Complete the following ANOVA table (to 2 decimals, if necessary). Round p-value to four decimal places.

1. The p-value for Factor A is:
2. What is your conclusion with respect to Factor A?
3. The p-value for Factor B
4. What is your conclusion with respect to Factor B?
5. The p-value for the interaction of factors A and B is
6. What is your conclusion with respect to the interaction of Factors A and B?
   

1. A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

Test for any significant differences due to language translator, type of language, and interaction (use a 5% significance level). Please write out all of your equations by hand.