Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was 15 inches. They wondered if the average vertical jump of students at their school differed from 15 inches, so they obtained a list of student names and selected a random sample of 20 students. After contacting these students several times, they finally convinced them to allow their vertical jumps to be measured. Here are the data (in inches): 11.0 11.5 12.5 26.5 15.0 12.5 22.0 15.0 13.5 12.0 23.0 19.0 15.5 21.0 12.5 23.0 20.0 8.5 25.5 20.5 A visual of the data distribution is below: Do these data provide convincing evidence at the α = 0.10 level that the average vertical jump of students at this school differs from 15 inches?

There is no convincing evidence at α = 0.10 level that the average vertical jump of students at this school differs from 15 inches.

Step-by-step explanation:

We have to make a hypothesis test to prove the claim that the average vertical jump of students differs from 15 inches.

The null and alternative hypothesis are:

The significance level is 0.10.

The sample mean is 17 and the sample standard deviation is 5.37.

The degrees of freedom are df=(20-1)=19.

The t-statistic is:

The two-sided P-value for t=1.67 is P=0.11132.

This P-value is bigger than the significance level, so the effect is not significant. The null hypothesis can not be rejected.

There is no convincing evidence at α = 0.10 level that the average vertical jump of students at this school differs from 15 inches.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for