BIOSTATISTICS ASSIGNMENT 6

1

Assignment 6 (Chapter 12) -- PH661

Spring 2021 Due Monday July 5th, 2021

Solve the following problems manually:

1. An employee at a local health center is concerned that there is a significant difference in

income between surgeons and other physicians employed at the facility. In order to test

this hypothesis, the employee collects a SRS of surgeons, and other physicians employed

by the health center, and compares their annual incomes. Assume the following table

represents the summary statistics for the investigation. Carry out the appropriate

statistical procedure to test the employee’s hypothesis at the alpha=0.05 level. Do not

assume equal variances. Carefully write out your null and alternative hypotheses, and

interpret your results.

Job Title Average Annual

Income

Standard Deviation Sample Size

Surgeon $235,287.00 6,549.00 32

All other physicians $164,875.00 8,024.00 41

2. Suppose a researcher is interested in the effectiveness in a new childhood exercise program implemented in a SRS of schools across a particular county. In order to test the

hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of

children from schools where the program is employed and a SRS from schools that do

not employ the program and compares the results. Assume the following table represents

the SRSs of students and their BMIs.

Student

Intervention Group

BMI (kg/m2) Student

Control Group

BMI (kg/m2)

A 18.6 A 21.6

B 18.2 B 18.9

C 19.5 C 19.4

D 18.9 D 22.6

E 24.1

F 23.6

A) Assuming that all the necessary conditions are met (normality, independence, etc.) carry out

the appropriate statistical test to determine if the new exercise program is effective. Use an alpha

level of 0.05. Do not assume equal variances.

B) Construct a 95% confidence interval about your estimate for the average difference in BMI

between the groups.

2

3. Food deserts have become a particularly hot topic in the public health community as an explanation for a variety of negative health outcomes in disadvantaged areas. A

researcher is interested in comparing the average shelf space provided by supermarkets,

convenience stores, and corner stores in two different communities in order to address the

growing concern for food deserts. Assume the following table reports the summary

statistics for shelf space dedicated to fresh fruits and vegetables (meters) from SRSs of a

variety of different stores that supply groceries from each community.

Community Average Shelf Space

for Fresh Fruits and

Vegetables (m)

Sample Standard

Deviation

Sample Size

“Food Desert” 13.7 2.4 12

Other Community 89.4 14.6 14

A) Carry out the appropriate statistical test in order to determine if there is a significant

difference in mean shelf space between the two communities at the alpha level of 0.05. Assume

all conditions for the test are met. Do not assume equal variances. Write out your null and

alternative hypotheses, and correctly interpret your pvalue.

B) Construct a 95% confidence interval for your estimate for the average difference in shelf

space provided for fresh fruits and vegetables. Provide an interpretation for your interval.

4. Recent publications have hinted at the growing importance of sleep in the elderly in order to maintain good health. Suppose a researcher is interested in the hypothesis that the

difference in average hours of sleep differs significantly between men aged 35-45 and

men aged 45+. Assume the following table summarizes the descriptive statistics for SRSs

from each age group. Carry out the appropriate statistical test to answer the researcher’s

hypothesis regarding the difference in average hours of sleep between the two groups

under investigation. Assume that all conditions for the testing are met. Use an alpha level

of 0.05. Calculate a pooled variance under the equal variance assumption. Write out your

null and alternative hypotheses and interpret your pvalue.

Age group Average hours of

sleep

Standard deviation Sample Size

35-45 7.4 1.02 24

45+ 5.2 0.87 32

3

5. Recent publications have addressed the growing concern in the scientific community around the increased prevalence of CAT scans in children between the ages of 7-18 and

the growing rate of childhood cancers. Suppose the researcher plans to gather a SRS from

a group of children in this age range who have received one or more CAT scans, and a

SRS from a group of children who have never received a CAT scan and compare the

number of cases of childhood cancers that develop over a prolonged period of time.

Assume the following table summarizes the descriptive statistics for his samples.

Population Average Cases of

Childhood Cancers

Standard Deviation Sample Size

≥1 CAT scan 24.6 2.4 1,894

No CAT scans 11.4 1.9 2,745

A) Carry out the appropriate statistical test to answer the researcher’s hypothesis regarding the

difference in average cases of childhood cancers in children aged 7-18 receiving one or more

CAT scans versus those that have never received a CAT scan. Use an alpha level of 0.05. Do not

use the equal variance assumption. Write out your alternative and null hypotheses, and interpret

your results.

B) Construct a 95% confidence interval for the average difference in childhood cancer cases

between the two groups. Interpret your interval.

6. International public health practitioners have continuously attempted to point out differences in smoking rates across the globe. Some say that smoking rates do not match

up with disease outcomes, i.e., countries that have the highest rates of smoking do not

have the highest rates of outcomes like lung and esophageal cancers. Suppose that a new

research team wants to observe the difference in average smoking rates between

Americans and French smokers. In order to test the assumption that French smokers

smoke less on the average than Americans, the researcher takes a SRS of smokers from

each country and compares their basic descriptive statistics for number of cigarettes

smoked per day. Assume the following table summarizes the findings.

Country Average Cigarettes

smoked per day

Standard deviation Sample Size

France 8.9 1.4 52

USA 8.7 3.1 46

A) Carry out the appropriate test to answer the research question that supposes that American

smokers smoke more cigarettes per day on the average than French smokers. Use an alpha level

of 0.05. Do not assume equal variances. Write out your null and alternative hypotheses, and

interpret your results.

B) Construct a 95% confidence interval for the difference in number of cigarettes smoked per

day between the two groups. Provide an interpretation for your interval.