For each statement/conclusion, choose the best pair of null hypothesis H0 and alternative hypothesis H1 in symbolic form. 1. IQ scores of statistics students have a standard deviation less than 15. A. H0:σ≤15, H1:σ>15 B. H0:σ≥15, H1:σ<15 C. H0:µ15 2. The mean salary of statistics professors is at most 70,000 dollars. A. H0:µ70,000, H1:µ≤70,000 C. H0:µ≥70,000, H1:µ70,000

1) For this case the correct option would be:

B. H0:σ≥15, H1:σ<15

Since they want to proof that the true deviation is less than 15 (alternative hypothesis) and the complement is on the null hypothesis.

2) For this case the correct option would be:

H0:µ≥70,000, H1:µ<70,000

Since they want to proof that the true mean salary is at most 70000 (alternative hypothesis) and the complement is on the null hypothesis.

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

1. IQ scores of statistics students have a standard deviation less than 15.

For this case the correct option would be:

B. H0:σ≥15, H1:σ<15

Since they want to proof that the true deviation is less than 15 (alternative hypothesis) and the complement is on the null hypothesis.

2. The mean salary of statistics professors is at most 70,000 dollars

For this case the correct option would be:

H0:µ≥70,000, H1:µ<70,000

Since they want to proof that the true mean salary is at most 70000 (alternative hypothesis) and the complement is on the null hypothesis.