Question

The proportion of Americans who have frequent migraines is 15.2% according to the CDC. An acupuncturist claims that her treatment can reduce this figure significantly. A random sample of 521 Americans is administered the acupuncturists treatment and 73 report experiencing migraines.

a. State Hypotheses to the scenario using the correct symbols.

b. What is the sample proportion? (Round to 2 decimal places) p^=

c. Suppose the P-value is calculated to be 0.0129
What would your decision be for this test using α=α= 0.025?

• a.fail to reject the null
• b.reject the null
• c.accept the null

d. Write a conclusion in terms of the acupuncturist's claim. Use the model provided by the instructor. Assume no errors were made.

Answer 1

a)

H0: p = 0.152

Ha: p < 0.152

b)

Sample proportion = 73 / 521 = 0.14

c)

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.14 - 0152 ) / sqrt [ 0.152 ( 1 - 0.152) / 521 ]

= -0.76

p-value = P(Z < z)

=P(Z < -0.76)

= 0.2236

d)

Since p-value > 0.025 , Fail to reject the null

e)

Conclusion -

We fail to support the claim that her treatment can reduce this figure significantly.