Question

(17) Homeowners claim that the mean speed of automobiles traveling on their street is greater than 35 mph. A random sample of 100 automobiles has a mean speed of 36 mph. Assume the population standard deviation is 4 mph. Since your friend lives on this street, you decide to test this claim to see if it is true. (Gi) State the null and alternative hypotheses. ii) Calculate the P-value for this test. (iii Is there enough evidence to support this claim at a 0.05?

Answer 1

a)

H0: $\mu$ <= 35

Ha: $\mu$ > 35

b)

Test statistics

z = $\bar{x}$ - $\mu$ / ($\sigma$ / sqrt(n) )

= 36 - 35 / (4 / sqrt(100) )

= 2.5

p-value = P( Z > z)

= P( Z > 2.5)

= 0.0062

c)

Since p-value < 0.05 significance level, we have enough evidence to support the claim.