Question

Fans seemed upset by the 2018 NASCAR rule changes, claiming that drivers had to be too careful when passing, so no one is racing for the lead. Before the changes, drivers were averaging 31.1 Quality Passes per race (250 laps). A sample of 13 drivers from 2018 showed an average of 25.3 QP, with a Standard Deviation of 14.9. We decide to run a Hypothesis Test to see if the QP statistic did change from 2017 to 2018.

a) What are the Hypotheses for our Test?

b) Calculate the Test Statistic. What is its P-value? If the Level of Significance is 5%, what should we conclude?

c) The Director seems unconvinced. Build a 95% Confidence Interval with the Sample and tell how it relates to the Hypothesis Test.

d) Worrying about making a wrong decision, the Director (who does not really know NASCAR) asks about the errors in Hypothesis Tests. Describe a Type 1 error and its Probability. What about a Type 2 error? How does its Probability relate to Type 1?

Answer 1

Average Quality pass, = 31.1

= 25.3

s = 14.9

n = 13

a)

Null hypothesis, H0: = ​​​​​​

Alternate hypothesis, Ha:​​​​​​

b)

​​​​​​

t = -1.4035

Df = n-1 = 13-1 = 12

P(t<-1.4035) = 0.0929​

Conclusion :​​

At 0.05 level of significance, we cannot reject the null hypothesis since p value is grewter than level of significance.

c)

,

Where t at 95% confidence interval = 1.782

C. I. = [17.93 , 32. 66]

d)

Type 1 error is the probability of rejecting a true null hypothesis. Which is alpha a = 0.05

Type 2 error is the probability of not rejecting a false null hypothesis. If p value is greater than type 1 error than the type 2 error will be p-type1 error.