26 Jan Can we expect Bill’s distribution

Mid-Term

Question 1

For each of the following settings (i) identify the variable ( s) in the study. ( ii) for each variable tell the type of variable ( e.g., categorical and ordinal, discrete, etc.) ( iii) identify the observational unit ( the thing sampled) , and (iv) determine the sample size.

A palaeontologist measured the width ( in mm) of the last upper molar in 36 specimens of the extinct mammal Acropithecus rigidus. ( list 4)

Question 2

For each of the following settings (i) identify the variable ( s) in the study. ( ii) for each variable tell the type of variable ( e.g., categorical and ordinal, discrete, etc.) ( iii) identify the observational unit ( the thing sampled) , and (iv) determine the sample size.

The birthweight, date of birth, and mother’s race were recorded for each of 65 babies. ( list 4)

Question 3

For each of the following settings (i) identify the variable ( s) in the study. ( ii) for each variable tell the type of variable ( e.g., categorical and ordinal, discrete, etc.) ( iii) identify the observational unit ( the thing sampled) , and (iv) determine the sample size.

A physician measured the height and weight of each of 37 children. ( list 4)

Question 4

Invent a sample of size 5 for which the sample mean is 20 and not all the observations are equal.

Question 5

Invent a sample of size 5 for which the sample mean is 20 and the sample median is 15>

Question 6

Ten patients with high blood pressure participated in a study to evaluate the effectiveness of the drug Timolol in reducing their blood pressure. The accompanying table shows systolic blood pressure measurements taken before and after 2 weeks of treatment with Timolol. Calculate the mean and AD of the change in blood pressure (note that some values are negative)

Blood Pressure ( mm HG)

Patient Before After Change

1 172 159 -13

2 186 157 -29

3 170 163 -7

4 205 207 2

5 174 164 -10

6 184 141 -43

7 178 182 4

8 156 171 15

9 190 177 -13

10 168 138 -30

Question 7

In a study of the relationship between health risk and income, a large group of people living in Massachusetts were asked a series of questions. Some of the results are shown in the following table.

Income

Low Medium High Total

Smoke 634 332 247 1,213

Don’t smoke 1,846 1,622 1,868 5,336

Total 2,480 1,954 2,115 6,549

(a) What is the probability that someone in this study smokes? Calculate your answers

(b) What is the conditional probability that someone in this study smokes, given the person has high income?

(c) Is being a smoker independent of having a high income? Why or why not?

Question 8

Suppose a certain population of observations is normally distributed. What percentage of the observations in the population.

(a) are within + 1.5 standard deviations of the mean?

(b) are more that 2.5 standard deviations above the mean?

(c) are more that 3.5 standard deviations away from ( above or below) the mean?

Question 9

In an agricultural experiment, a large uniform field was planted with a single variety of wheat. The field was divided into many plots ( each plot being 7 X 100 ft) and the yield (lb) of grain was measured for each plot. These plot yields followed approximately a normal distribution with mean 88 lb and standard deviation 7 ib. What percentage of the plot yields were

(a) 80 lb or more?

( b) 90 lb or more?

(c) 75 lb or less?

Question 10

In the United States, 44% of the population has type O blood. Suppose a random sample of 12 persons is taken. Find the probability that 6 of the persons will have type O blood ( and 6 will not)

Question 11

Suppose that every day for 3 months Bill takes a random sample of 20 college students, records the number of calories they consume on that day., finds the average of the 20 observations, and adds the average to his histogram of the sampling distribution of the mean.

Suppose also that every day for 2 months Susan takes a random sample of 30 college students and records the number of calories they consume on that day ( which is fairly symmetric), finds the average of the 30 observations, and adds the average to her histogram of the sampling distribution of the mean.

(a) Can we expect Bill’s distribution and Susan’s distribution to haver the same shape? Why or Why not? If not, how will the shape differ?

Question 12

Suppose that every day for 3 months Bill takes a random sample of 20 college students, records the number of calories they consume on that day., finds the average of the 20 observations, and adds the average to his histogram of the sampling distribution of the mean.

Suppose also that every day for 2 months Susan takes a random sample of 30 college students and records the number of calories they consume on that day ( which is fairly symmetric), finds the average of the 30 observations, and adds the average to her histogram of the sampling distribution of the mean.

Can we expect Bill’s distribution and Susan’s distribution to have the same center? Why or why not? If not, how will the centers differ?

Question 13

Suppose that every day for 3 months Bill takes a random sample of 20 college students, records the number of calories they consume on that day., finds the average of the 20 observations, and adds the average to his histogram of the sampling distribution of the mean.

Suppose also that every day for 2 months Susan takes a random sample of 30 college students and records the number of calories they consume on that day ( which is fairly symmetric), finds the average of the 30 observations, and adds the average to her histogram of the sampling distribution of the mean.

Can we expect Bill’s distribution and Susan’s distribution to have the same spread? Why or why not? If not, how will the spreads differ?

Question 14

True or false ( and state why) We are 95% confident that? y1 is greater that y2, since most of the confidence interval is greater than zero.

Question 15

True or False ( and say why): We are 95% confident that the difference between y1 and y2 is between – 2.3 days and 16.1 days.

Question 16

True or False ( and say why): 95 % of the nitric oxide infants were hospitalized longer than the mean of the control infants.