Question

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:µ<15, H1:µ≥15 D. H0:µ≤15, H1:µ>15 2. The mean salary of statistics professors is at most 70,000 dollars. A. H0:µ<70,000, H1:µ≥70,000 B. H0:µ>70,000, H1:µ≤70,000 C. H0:µ≥70,000, H1:µ<70,000 D. H0:µ≤70,000, H1:µ>70,000 3. More than one-half of all Internet users make on-line purchases. A. H0:µ≥0.5, H1:µ<0.5 B. H0:µ≤0.5, H1:µ>0.5 C. H0:p≥0.5, H1:p<0.5 D. H0:p≤0.5, H1:p>0.5

Answer 1

Answer:

1) For this case we want to check if the population deviation is less than 15( alternative hypothesis) and the system of hypothesis are:

H0: $\sigma \geq 15$

H1: $\sigma$

B. H0:σ≥15, H1:σ<15

2) For this case we want to check if the population mean $\mu$ is at most 70000 (alternative hypothesis) and the system of hypothesis are:

H0: $\mu \geq 70000$

H1: $\mu$

C. H0:µ≥70,000, H1:µ<70,000

3) For this case we want to check if the population proportion $p$ of all internet users that make online purchases is higher than 0.5 (alternative hypothesis) and the system of hypothesis are:

H0: $p \leq 0.5$

H1: $p >0.5$

D. H0:p≤0.5, H1:p>0.5

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) For this case we want to check if the population deviation is less than 15( alternative hypothesis) and the system of hypothesis are:

H0: $\sigma \geq 15$

H1: $\sigma$

B. H0:σ≥15, H1:σ<15

2) For this case we want to check if the population mean $\mu$ is at most 70000 (alternative hypothesis) and the system of hypothesis are:

H0: $\mu \geq 70000$

H1: $\mu$

C. H0:µ≥70,000, H1:µ<70,000

3) For this case we want to check if the population proportion $p$ of all internet users that make online purchases is higher than 0.5 (alternative hypothesis) and the system of hypothesis are:

H0: $p \leq 0.5$

H1: $p >0.5$

D. H0:p≤0.5, H1:p>0.5