Speeding: On a certain stretch of West Street, I claim that most cars are going

Question

Speeding: On a certain stretch of West Street, I claim that most cars are going more than 5 miles per hour (mph) over the speed limit. The speed limit is posted at 25 mph. In a random sample of 80 cars, 52 of them were traveling faster than 30 mph. Test my claim at the 0.01 significance level.

(a) What is the sample proportion of cars going more than 5 mph over the speed limit? Round your answer to 3 decimal places.

p =

(b) What is the test statistic? Round your answer to 2 decimal places.

zp hat =

(c) What is the P-value of the test statistic? Round your answer to 4 decimal places.

P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H0

fail to reject H0

(e) Choose the appropriate concluding statement.

The data supports the claim that most cars are traveling more than 5 mph over the speed limit.

There is not enough data to support the claim that most cars are traveling more than 5 mph over the speed limit.

We reject the claim that most cars are traveling more than 5 mph over the speed limit.

We have proven that most cars are traveling more than 5 mph over the speed limit.

Explanation / Answer

Ans:

Most cars means that proportion of overspeeding cars is more than 0.5

a)sample proportion=52/80=0.65

b)Test statistic:

z=(0.65-0.5)/sqrt(0.5*(1-0.5)/80)=2.68

c)p-value=P(z>2.68)=0.0036

d)As,p-value<0.01,we reject null hypothesis.

e)The data supports the claim that most cars are traveling more than 5 mph over the speed limit.

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