Question

Self-Reported Weight. The article "Accuracy of SelfReported Height and Weight in a Community-Based Sample of C)der African Americans and Whites" (Joumal of Gerontology Series A: Biological Sciences and Medical Sciences, Vol. 65A, No. 10, Pp. 1123-1129) by G. Fillenbaum et al. explores the relationship between measured and self-reported height and weight. The authors sampled African American and White women and men older than 70 years of age. A hypothesis test is to be performed to decide whether, on average, self-reported weight is less than measured weight for the aforementioned age group.

a. identify the variable.

b. identify the two populations:

c. identify the pairs

d. identify the paired-diffenence variable.

e. determine the null and allernative hypotheses.

f. classify the hypothesis test as nwo tailed, left tailed, or right tailed.

Short answer

Part a)the variable is "weight"

Part b) the two populations in the study are "self reported weight" and "actual weight of women and men over 70".

Part c)the pair is a "self reported weight and actual weight of women and men over 70

Part d)$\text{Paired difference variable}=(\text{Self reported weight}-\text{Actual weight})$

Part e)the null and alternative hypotheses.

Part f) the hypotheses test as left tailed test

Step-by-step solution

Step 1:Given information

Self-Reported Weight. The article "Accuracy of SelfReported Height and Weight in a Community-Based Sample of C)der African Americans and Whites" (Joumal of Gerontology Series A: Biological Sciences and Medical Sciences, Vol. 65A, No. 10, Pp. 1123-1129) by G. Fillenbaum et al. explores the relationship between measured and self-reported height and weight. The authors sampled African American and White women and men older than 70 years of age. A hypothesis test is to be performed to decide whether, on average, self-reported weight is less than measured weight for the aforementioned age group.

Step 2:Explaination Part a)

Identify the variable in the study.

A variable is an attribute or the characteristic that can be measured. The value of the variable may differ for each and every unit. That is, a variable is defined as the characteristic which is recorded for each case.

From the given description, the variable is "weight" because the outcome for each attempt can be measured and this value may vary for each and every attempt.

Step 2:Explaination Part b)

Identify the two populations:

Population:

The population is the complete set of people who are considered for the study.

Therefore, the two populations in the study are "self reported weight" and "actual weight of women and men over 70".

Step 2:Explaination Part c)

Identify the pairs.

Here, the pair is a "self reported weight and actual weight of women and men over 70 " because the samples of weights taken from persons and divided into self reported weight and actual weight.

Step 2:Explaination Part d)

Identify the paired difference variable.

The paired difference variable is "the difference between the self reported weight and the actual weight". That is,

$\text{Paired difference variable}=(\text{Self reported weight}-\text{Actual weight})$

Step 2:Explaination Part e)

State the null and alternative hypotheses.

Null hypothesis:

$H_0:{\mu }_1={\mu }_2$

That is, the average self reported weight is not less than the measured weight for the aforementioned age group.

Alternative hypothesis:

$H_a:{\mu }_1<{\mu }_2$

That is, the average self reported weight is less than the measured weight for the aforementioned age group.

Step 2:Explaination Part f)

Classify the hypotheses test as two tailed, left tailed, or right tailed.

From part (e), it is clear that the hypotheses test as left tailed test because the average self reported weight is less than the measured weight for the aforementioned age group.