Question

(14) 1. The average time to run a race is 14 minutes. You wish to see if a new training regimen will lower the time to run the race. After doing the training regimen you run the race 35 times and the average time to run the race now is 13.32 minutes with a standard deviation of 1.4 minutes.

a) At the .05 level did the training regimen lower the time (note: p value from computer is p = .003)

b) Based on the answer for a) did the training regimen lower the time? (yes or no) Answer:

c) What is the only type of error that could have occurred

Answer:

D) Interpret the p-value: Answer:

E) How do you explain the .68 minutes lowering of the time Answer:

Answer 1

(a)

H0: Null Hypothesis: 14 ( the training regimen did not lower the time)

HA: Alternative Hypothesis: 14 ( the training regimen lowered the time) (claim)

= 13.32

s = 1.4

n = 35

df = 35 - 1 = 34

= 0.05

From Table,critical value of t = - 1.69

test Statistic is given by:

p value from computer is p = 0.003

Since p - value = 0.003 is less than = 0.05,, the differene is significant. Reject null hypothesis.

Conclusion:
The data support that claim that the training regimen lowered the time.

(b)

Correct option:

Yes

(c)

Since in this hypothesistest, we have rejected the null hypothesis, the only type of error that could have occurred :

Type I Error: Rejection of a true null hypothesis

(d)

P - value = 0.003 is the probability for the given statistical model that when the null hypothesis: the training regimen did not lower the time is true, the statistical summary would be equal to or mre extreme than the actual observed results.

AS PER DIRECTIONS FOR ANSWERING, FIRST 4 QUESTIONS ARE ANSWERED.