Question

6.73 Hypotheses. In each of the following situations,
state an appropriate null hypothesis H0 and alternative
hypothesis Ha. Be sure to identify the parameters
that you use to state the hypotheses. (We have not yet
learned how to test these hypotheses.)
(a) A sociologist asks a large sample of high school
students which academic subject they like best. She
suspects that a higher percent of males than of females
will name economics as their favorite subject.
(b) An education researcher randomly divides
sixth-grade students into two groups for physical
education class. He teaches both groups basketball skills,
using the same methods of instruction in both classes.
He encourages Group A with compliments and other
positive behavior but acts cool and neutral toward Group
B. He hopes to show that positive teacher attitudes result
in a higher mean score on a test of basketball skills than
do neutral attitudes.
(c) An economist believes that among employed
young adults, there is a positive correlation between
income and the percent of disposable income that is
saved. To test this, she gathers income and savings
data from a sample of employed persons in her city
aged 25 to 34.

Answer 1

(a) Let µ₁ be males.

Let µ₂ be females.

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ > µ₂

(b) Let µ₁ be Group A students.

Let µ₂ be Group B students.

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ > µ₂

(c) The hypothesis being tested is:

H₀: ρ = 0

H_a: ρ ≠ 0

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