Question

For each of the following claims, fill in the blanks in the provided hypotheses with inequalities. If your answer is "less than," type: < If your answer is "greater than," type: > If your answer is "less than or equal to," type: <= If your answer is "greater than or equal to," type: >= If your answer is "equal to," type: = If your answer is "not equal to," type: /= (a) Theory to be tested: The average number of children per household in the United States is less than 3. H0: μ 3 and Ha: μ 3 (b) Theory to be tested: The average weight of TAMU students is greater than 110 pounds. H0: μ 110 and Ha: μ 110 (c) Theory to be tested: The average diameter of Saguaro cacti is not 2.1 feet. H0: μ 2.1 and Ha: μ 2.1 (d) Theory to be tested: In Belarus (former member of the Soviet Union, located near Chernobyl), the average life span is under 70 years. H0: μ 70 and Ha: μ 70

Answer 1

Answer:

a) H0: μ=>3; Ha: μ<3

b) H0: μ<=110; Ha: μ>110

c) H0: μ=2.1; Ha: μ/=2.1

d) H0: μ=>70; Ha: μ<70

Step-by-step explanation:

The claims are usually expressed in the alternative hypothesis, for which we evaluate the evidence, usually sample statistics.

(a) Theory to be tested: The average number of children per household in the United States is less than 3.

In this case, the claim is that the mean is below 3 children per household. The null hypothesis will state then that the average number of children is 3 or more.

H0: μ=>3; Ha: μ<3

(b) Theory to be tested: The average weight of TAMU students is greater than 110 pounds.

The alternative hypothesis represents the claim that the mean is greater than 110. The null hypothesis, then will state that the mean is equal or less than 110.

H0: μ<=110; Ha: μ>110

(c) Theory to be tested: The average diameter of Saguaro cacti is not 2.1 feet.

In this case, the alternative hypothesis is represented by an unequal sign (the average diameter can be higher or lower). Then, the null hypothesis will state that the average diameter is equal to 2.1.

H0: μ=2.1; Ha: μ/=2.1

(d) Theory to be tested: In Belarus (former member of the Soviet Union, located near Chernobyl), the average life span is under 70 years.

The alternative hypothesis states that the average life span is under 70 years, so the null hypothesis will state that it is equal or more than 70 years.

H0: μ=>70; Ha: μ<70