Question

9. A chiropractic school states that 56% of adult Americans have back pain. A prominent chiropractor disputes that claim; she thinks the real percentage is lower. She conducts a random sample of 200 adult Americans and determines that 104 of them had back pain. Using a 2% significance level, conduct all steps of a hypothesis test to test the local chiropractor’s belief.

Answer 1

H₀: p = 0.56

H₁: p < 0.56

= 104/200 = 0.52

The test statistic is

  

P-value = P(Z < -1.14)

             = 0.1271

Since the P-value is greater than the significance level(0.1271 > 0.02), so we should not reject the null hypothesis.

At 0.02 significance level, there is not sufficient evidence to support the local chiropractor's belief that the real percentage of adult Americans who have back pain is less than 0.56.