Question

An article measured speeds of vehicles on several roads in the state of Kansas. On South Cedar Niles, 73 vehicles were observed, and 49 of them were exceeding the speed limit. Can you conclude that more than half of the vehicles on South Cedar Niles exceed the speed limit? Find the P-value and state a conclusion.

Answer 1

The sample supports the hypothesis that more than half of the vehicles in South Cedar Niles exceed the speed limit.

p-value = 0.00092

Explanation:

To solve this problem, we run a hypothesis test about the population proportion.

Proportion in the null hypothesis
`\pi_0 = 0.5`

Sample size (n) = 73

Sample proportion (p) = 49/73 = 0.6712

H0:
`\pi_0 = 0.5`

Ha:
`\pi_0 \geq 0.5`

Test statistic =
`(p - pi)√(n) / √(\pi_0 (1-\pi_0))`

Calculated statistic =
`(0.6712 - 0.5)√(73) / \sqrt {0.5(1-0.5)} = 2.9255`

p-value = 0.00092

Since, p - value is less than or equal to 0.05, the null hypothesis must be rejected. The sample supports the hypothesis that more than half of the vehicles in South Cedar Niles exceed the speed limit.