Question

In Exercises 10.25-10.30, hypothesis tests are proposed. For each

hypothesis test,

a. identify the variable.

b. identify the two populations,

c. determine the null and alternative hypotheses.

d. classify the hypothesis test as two tailed, left tailed, or right tailed.

Children of Diabetic Mothers. Samples of adolescent offspring of diabetic mothers (ODM) and nondiabetic mothers (ONM) were taken by N. Cho et al. and evaluated for potential differences in vital measurements, including blood pressure and glucose tolerance. The study was published in the paper "Correlations Between the Intrauterine Metabolic Environment and Blood Pressure in Adolescent Offspring of Diabetic Mothers" (Journal of Pediatrics, Vol. 136, Issue 5. pp. 587-592). A hypothesis test is to be performed to decide whether the mean systolic blood pressure of ODM adolescents exceeds that of ONM adolescents.

Short answer

Part a. The variable in this study is systolic blood pressure.

Part b. The two populations in this study are adolescent offspring of diabetic mothers (ODM) and nondiabetic mothers (ONM).

Part c. Null Hypothesis $H_0:{\mu }_1={\mu }_2$

and alternative hypothesis $H_a:{\mu }_1>{\mu }_2$

Part d. The hypothesis test is right tailed test.

Step-by-step solution

Part (a) Step 1. Given Information

We have been proposed a hypothesis test.

A hypothesis test is to be performed to decide whether the mean systolic blood pressure of ODM adolescents exceeds that of ONM adolescents.

Part (a) Step 2. Identify the variable

A variable is an attribute or a 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.

In the given study, systolic blood pressure was measured. It is clear that systolic blood pressure varies from person to person. Hence, the variable is systolic blood pressure

Part (b) Step 1. Identify the two populations

The population includes all the individuals of interest that are being examined. In other words, the collection of all people, items, or objects that are required for a specific study is defined as the population.

Here, the given study involves adolescent offspring of diabetic mothers (ODM) and nondiabetic mothers (ONM). Thus, the population is all adolescent offspring of diabetic mothers (ODM) and nondiabetic mothers (ONM).

Part (c) Step 1. Determine the null and alternative hypothesis

Let us assume that ${\mu }_1$denotes the mean systolic blood pressure of ODM adolescents and ${\mu }_2$denotes the mean systolic blood pressure of ONM adolescents.

The null hypothesis is defined as

$H_0$: There is no significant difference between the mean systolic blood pressure of ODM and ONM adolescents.

role="math" localid="1652709845512" $H_0:{\mu }_1={\mu }_2$

The alternative hypothesis is defined as

$H_a:$The mean systolic blood pressure of ODM adolescents exceeds that of ONM adolescents.

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

Part (d) Step 1. Classification

As our alternative hypothesis suggest that the mean of the first population is greater than the mean of the second population.

So the hypothesis can be classified as right-tailed test.