Question

The correct answers are highlighted. I would like an explanation for why some are null hypothesis and some are alternative. Thank you.

4	You are testing the hypothesis that the mean textbook expense per semester at IUPUI is at least $500. The null and alternative hypothesis statements for this test are:
a	H₀:	μ ≤ 500	H₁:	μ > 500
b	H₀:	μ ≥ 500	H₁:	μ < 500
c	H₀:	μ < 500	H₁:	μ ≥ 500
d	H₀:	μ > 500	H₁:	μ ≤ 500
5	You are testing the hypothesis that the mean commuting time to the IUPUI campus is less than 20 minutes. The null and alternative hypothesis statements for this test are:
a	H₀:	μ ≤ 20	H₁:	μ > 20
b	H₀:	μ ≥ 20	H₁:	μ < 20
c	H₀:	μ < 20	H₁:	μ ≥ 20
d	H₀:	μ > 20	H₁:	μ ≤ 20
6	You are testing the hypothesis that the mean student commuting distance to the IUPUI campus is at most 10 miles. The null and alternative hypothesis statements for this test are:
a	H₀:	μ < 10	H₁:	μ ≥ 10
b	H₀:	μ > 10	H₁:	μ ≤ 10
c	H₀:	μ ≤ 10	H₁:	μ > 10
d	H₀:	μ ≥ 10	H₁:	μ < 10

Answer 1

Null hypothesis always contain , = , and signs.

The null hypothesis H0 and alternative hypotheses H1 are complementary.  

Question 4)

You are testing the hypothesis that the mean textbook expense per semester at IUPUI is at least $500.

At least $ 500 is claim and it is null hypothesis

At least means

b

H₀:

μ ≥ 500

H₁:

μ < 500

Question 5) You are testing the hypothesis that the mean commuting time to the IUPUI campus is less than 20 minutes.

less than 20 minutes (Claim ) it is in alternative hypothesis.

b

H₀:

μ ≥ 20

H₁:

μ < 20

Question 6)  You are testing the hypothesis that the mean student commuting distance to the IUPUI campus is at most 10 miles.

at most 10 miles (Claim)

at most means contain

c

H₀:

μ ≤ 10

H₁:

μ > 10