The proportion of Americans who have frequent migraines is 15.2% according to th
ID: 3369292 • Letter: T
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 232 Americans is administered the acupuncturists treatment and 30 report experiencing migraines.
a. State Hypotheses to the scenario using the correct symbols.
b. What is the sample proportion? (Round to 2 decimal places) ˆp^=
c. Suppose the P-value is calculated to be 0.0098
What would your decision be for this test using ?= 0.01?
A)accept the null
B)reject the null
C)fail to reject 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.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.152
Alternative hypothesis: P < 0.152
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.02357
z = (p - P) / S.D
z = - 0.963
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 0.963.
Thus, the P-value = 0.168
Interpret results. Since the P-value (0.168) is more than the significance level (0.01), we have to accept the null hypothesis.
C) Fail to reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim treatment can reduce this figure significantly.
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