Question

Some of the statements below refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p).

A. The mean number of years Americans work before retiring is 34. (out of the following)

H₀: p = 34,     H_a: p ≠ 34

H₀: μ = 34,     H_a: μ ≠ 34     

H₀: p ≥ 34,     H_a: p < 34

H₀: p ≤ 34,     H_a: p > 34

H₀: μ ≤ 34,     H_a: μ > 34

H₀: μ ≠ 34,     H_a: μ = 34

H₀: μ ≥ 34,     H_a: μ < 34

H₀: p ≠ 34,     H_a: p = 34

B. At most 60% of Americans vote in presidential elections. (Out of the following)

H₀: p ≤ 0.60,     H_a: p > 0.60

H₀: p > 0.60,     H_a: p ≤ 0.60     

H₀: p = 0.60,     H_a: p > 0.60

H₀: μ = 60,     H_a: μ > 60

H₀: μ < 60,     H_a: μ > 60

H₀: μ > 60,     H_a: μ ≤ 60

H₀: p < 0.60,     H_a: p > 0.60

H₀: μ ≤ 60,     H_a: μ > 60

C. The mean starting salary for San Jose State University graduates is at least $100,000 per year. (out of the following)

H₀: p = 100,000,     H_a: p < 100,000

H₀: μ = 100,000,     H_a: μ < 100,000     

H₀: p < 100,000,     H_a: p ≥ 100,000

H₀: μ ≥ 100,000,     H_a: μ < 100,000

H₀: p ≤ 100,000,     H_a: p > 100,000

H₀: μ < 100,000,     H_a: μ ≥ 100,000

H₀: μ ≤ 100,000,     H_a: μ > 100,000

H₀: p ≥ 100,000,     H_a: p < 100,000

D. Twenty-nine percent of high school seniors get drunk each month. (out of the following)

H₀: p < 0.29,     H_a: p > 0.29

H₀: μ = 29,     H_a: μ ≠ 29     

H₀: p ≠ 0.29,     H_a: p = 0.29

H₀: p = 0.29,     H_a: p > 0.29

H₀: μ = 29,     H_a: μ > 29

H₀: μ ≠ 29,     H_a: μ = 29

H₀: μ < 29,     H_a: μ > 29

H₀: p = 0.29,     H_a: p ≠ 0.29

E. Fewer than 5% of adults ride the bus to work in Los Angeles. (out of the following)

H₀: μ ≥ 5,     H_a: μ < 5

H₀: p ≥ 0.05,     H_a: p < 0.05     

H₀: p = 0.05,     H_a: p ≠ 0.05

H₀: μ < 5,     H_a: μ ≥ 5

H₀: p ≤ 0.05,     H_a: p > 0.05

H₀: μ ≤ 5,     H_a: μ > 5

H₀: p < 0.05,     H_a: p ≥ 0.05

H₀: μ = 5,     H_a: μ ≠ 5

F. The mean number of cars a person owns in her lifetime is not more than 10. (out of the following)

H₀: p = 10,     H_a: p ≠ 10

H₀: μ ≥ 10,     H_a: μ < 10     

H₀: p ≥ 10,     H_a: p < 10

H₀: μ ≤ 10,     H_a: μ > 10

H₀: p ≤ 10,     H_a: p > 10

H₀: μ = 10,     H_a: μ ≠ 10

H₀: μ < 10,     H_a: μ ≥ 10

H₀: p < 10,     H_a: p ≥ 10

G. About half of Americans prefer to live away from cities, given the choice.

H₀: p ≠ 0.50,     H_a: p = 0.50

H₀: μ = 1/2 , H_a: μ ≠ 1/2

H₀: p ≥ 0.50,     H_a: p < 0.50

H₀: p = 0.50,     H_a: p ≠ 0.50

H₀: μ ≥ 1/2 , H_a: μ = 1/2

H₀: μ ≠ 1/2 , _Ha: μ < 1/2

H₀: p ≤ 0.50,H_a: p > 0.50

H₀: μ ≤ 1/2 ,     H_a: μ > 1/2

H. Europeans have a mean paid vacation each year of six weeks. (out of the following)

H₀: p ≠ 6,     H_a: p = 6

H₀: μ ≥ 6,     H_a: μ < 6     

H₀: p = 6,     H_a: p ≠ 6

H₀: μ ≤ 6,     H_a: μ > 6

H₀: p ≤ 6,     H_a: p > 6

H₀: p ≥ 6,     H_a: p < 6

H₀: μ ≠ 6,     H_a: μ = 6

H₀: μ = 6,     H_a: μ ≠ 6

I. The chance of developing breast cancer is under 11% for women. (Out of the following)

H₀: μ < 11,     H_a: μ ≥ 11

H₀: μ ≤ 11,     H_a: μ > 11     

H₀: p < 0.11,     H_a: p ≥ 0.11

H₀: p ≤ 0.11,     H_a: p > 0.11

H₀: p = 0.11,     H_a: p ≠ 0.11

H₀: μ ≥ 11,     H_a: μ < 11

H₀: μ = 11,     H_a: μ ≠ 11

H₀: p ≥ 0.11,     H_a: p < 0.11

J. Private universities' mean tuition cost is more than $20,000 per year. (out of the following)

H₀: μ ≥ 20,000,     H_a: μ < 20,000

H₀: p > 20,000,     H_a: p ≤ 20,000    

H₀: p ≥ 20,000,     H_a: p < 20,000

H₀: p ≤ 20,000,     H_a: p > 20,000

H₀: μ ≤ 20,000,     H_a: μ > 20,000

H₀: μ = 20,000,     H_a: μ ≠ 20,000

H₀: μ > 20,000,     H_a: μ ≤ 20,000

H₀: p = 20,000,     H_a: p ≠ 20,000

Answer 1

A. Here claim is that the mean number of years Americans work before retiring is 34.

As null hypothesis always have equality sign.

Answer here is

H0: μ = 34,     Ha: μ ≠ 34     

B. Here claim is that At most 60% of Americans vote in presidential elections.

As null hypothesis always have equality sign.

Answer here is

H0: p ≤ 0.60,     Ha: p > 0.60

C. Here claim is that the mean starting salary for San Jose State University graduates is at least $100,000 per year.

As null hypothesis always have equality sign.

Answer here is

H0: μ ≥ 100,000,     Ha: μ < 100,000

D. Here claim is that Twenty-nine percent of high school seniors get drunk each month.

As null hypothesis always have equality sign.

Answer here is

H0: p = 0.29,     Ha: p ≠ 0.29

E. Here claim is that fewer than 5% of adults ride the bus to work in Los Angeles.

As null hypothesis always have equality sign.

Answer here is

H0: p ≥ 0.05,     Ha: p < 0.05     

F. Here claim is that the mean number of cars a person owns in her lifetime is not more than 10.

As null hypothesis always have equality sign.

Answer here is

H0: μ ≤ 10,     Ha: μ > 10

G. Here claim is that about half of Americans prefer to live away from cities.

As null hypothesis always have equality sign.

Answer here is

H0: p = 0.50,     Ha: p ≠ 0.50

H. Here claim is that Europeans have a mean paid vacation each year of six weeks

As null hypothesis always have equality sign.

Answer here is

H0: μ = 6,     Ha: μ ≠ 6

I. Here claim is that The chance of developing breast cancer is under 11% for women.

As null hypothesis always have equality sign.

Answer here is

H0: p ≥ 0.11,     Ha: p < 0.11

J. Here claim is that Private universities' mean tuition cost is more than $20,000 per year.

As null hypothesis always have equality sign.

Answer here is

H0: μ ≤ 20,000,     Ha: μ > 20,000