Question

The posted speed limit along Elm Street is 25 mph. Homeowners living on Elm Street claim that the

average speed of automobiles traveling on Elm Street is greater than the posted limit of 25 mph and plan to

investigate their claim by measuring the speed of 20 randomly selected cars. If the data support the claim,

the residents plan to ask the city council for more police patrol along Elm Street. Here are the speeds (in

mph) of the 20 cars:

26. 2 22. 9 28. 8 29. 0 24. 8

24. 7 24. 0 24. 4 25. 2 31. 1

25. 6 21. 6 27. 4 25. 6 26. 4

23. 7 28. 2 24. 1 26. 7 26. 8


(a) Is there convincing evidence at the a = 0. 05 significance level that the true mean speed of all cars

traveling on Elm Street is more than 25 mph?

(b) Referring to your conclusion, what type of error may have been made? Describe the error in the

context of this study

Answer 1

The sample of the speeds of 20 cars and at a 0.05 confidence level, we

have;

(a) There is not enough convincing evidence to suggest that the true mean speed of all cars travelling on Elm Street is more than 25 mph

(b) Type II error

What are the process to test the hypothesis?

(a) Based on the given data, using MS Excel, we have;

The sample size, n = 20

The mean, $\overline x$ = 25.86

The standard deviation of the sample, s = 2.284

The null hypothesis, H₀; $\overline x$ = 25 mph

Alternative hypothesis, Hₐ; $\overline x$ > 25 mph

Given that the sample size is less than 30, the t-test is used, and the t-score is found as follows;

$t= \mathbf{\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}}$

Which gives;

$t=\dfrac{25.86-25 }{\dfrac{2.284}{\sqrt{20}}} \approx \mathbf{1.684}$

Using a graphing calculator, we have;

The probability ≈  0.054

The critical-t ≈ 1.729

Given that the probability is larger than the significance level, we fail to

reject the null hypothesis.

There is not enough convincing statistical evidence to conclude that the

true mean of all cars travelling on Elm Street is more than 25 mph.

(b) The type of error is Type II error, given that there is a possibility that

the null hypothesis is failed to be rejected when it is actually false.

Given that the sample size is less than 30, it may be insufficient for the

Central Limit Theorem to be in effect.

Learn more about statistical hypothesis testing here:

https://brainly.com/question/14042255