Assignment Details

Subject: Mathematics / Statistics

Question

Assignment 7 -? Inference using t-?methods Problem 1: (21 points total) Is the average body temperature actually less than 98.6 degrees Fahrenheit for healthy human adults? A

sample of 21 healthy human adults was taken. The body temperature of each of these 21 individuals is

given in the bodytemps.csv data set on Canvas. Use these data to answer the following questions. (R

Tutorial 6 may be helpful in answering some of the questions.)

1. State the null and alternative hypotheses in notation. Define the notation used. (Be specific – make

sure the population is included when you define the notation.) (3 points)

2. Why is it appropriate to use the one-sample t-test in this problem? (Do not assess the conditions in

answering this question. Rather, refer to the “statistical bible” of when to use a t-test.) (2 points)

3. There are three conditions that must be satisfied for conclusions from the t-test to be valid to the

population of interest. Assess each of these conditions.

a. Condition 1: the sample is representative of the population. Note that there is not much

information about the make-up of the 21 individuals and how they were selected. Discuss what

would make these 21 “representative” of the population. (2 points)

b. Condition 2: the distribution of sample means is normal. You’ll need to include a graph to support

your assessment of this condition. (2 points)

c. Condition 3: the observations are independent of each other. Discuss what this condition means

in the context of the problem and whether or not you believe this conditions is true. (2 points)

4. Use R to obtain the t-statistic and p-value. Report the t-statistic (with degrees of freedom) and the pvalue here. Do NOT include the rest of the output! (2 points)

5. Interpret the p-value in the context of the problem. (Note: this is NOT asking for a conclusion. Think

about the definition of the p-value to answer this question.) (2 points)

6. State a conclusion in the context of the problem based on the p-value. If you had any concerns that

one or more of the conditions wasn’t satisfied, mention that here. (3 points)

7. Report AND interpret a 95% confidence interval for the mean body temperature in the population. (3

points) Problem 2: (14 points total) Can pleasant smells improve learning? Researchers performed an experiment in which 42 subjects were

randomly assigned to one of two comparison groups. Subjects assigned to the “treatment” group

completed a paper-and-pencil maze with the presence of a floral aroma. Subjects assigned to the control

group completed a paper-and-pencil maze without the presence of the floral aroma. All subjects were

timed as to how long it took them to complete the maze (in seconds). The data are given in the

aroma.csv data set on Canvas. Use these data to determine if there is evidence that the floral scent

improved the subjects’ ability to complete the maze? (That is, is the average time to complete the maze

faster in the presence of the floral aroma than without?)

Answer these questions to answer the question of interest. (Note: R tutorial 6 may be helpful in answering

some of these questions.)1. What is the response variable? Is it quantitative or categorical? (1 point)2. State the null and alternative hypotheses in notation and words. Define the notation. Don’t forget to

include the populations when defining the notation and when writing the hypotheses in words! (3

points)3. Obtain and include a properly labeled side-by-side box-and-whisker plot. From the box-and-whisker

plots, do you feel there is convincing evidence to indicate the presence of a floral aroma improves

subjects’ ability to complete the maze, on “average”? Explain answer these questions: (2 points – 1

point for properly labeled graph and 1 point for explanation)4. Use R to obtain the test-statistic and p-value. Report the test-statistic with degrees of freedom and

the p-value here. Do NOT include the rest of the output! (2 points)5. State a conclusion in the context of the problem based on the p-value. (3 points)6. Report and interpret a 90% confidence interval for the difference in the mean time to complete the

maze between those in the presence of the floral aroma and those not in the presence of the floral

aroma. (3 points)