Question

Business owners on Suffern Main street claim that the mean speed of automobiles traveling on their street is greater than the speed limit of 35 miles per hour. A Random sample of 100 automobiles was surveyed by a police radar operator. The sample yields a mean speed of 36 miles per hour and a standard deviation of 4 miles per hour.. Is there enough evidence to support the claim at α = 0.05 (use a P-value)
•a)Identify the claim. Then state the null and alternative hypotheses.
•b)Identify if it is a left , right tailed test or 2 tail test, level of significance and state the critical value
•c)Find the standardized test statistic z.
•d)Construct the rejected region and decide whether to reject the Null Hypothesis.
•e)Find the p-value
•f)Interpret the result in the context of the original claim

Answer 1

a)

claim : μ > 35

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 35
Alternative Hypothesis, Ha: μ > 35

b)

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.

c)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (36 - 35)/(4/sqrt(100))
z = 2.5

d)
Hence reject H0 if z > 1.645

reject the null hypothesis.

e)

P-value Approach
P-value = 0.0062

f)

There is enough evidence to support the claim