A teaching hospital in the District of Columbia has been working with residents
ID: 3131863 • Letter: A
Question
A teaching hospital in the District of Columbia has been working with residents to reduce heart disease deaths in the district. To verify their efforts, they surveyed 320 recent death certificates and got 64 that were caused by heart disease. Use a significance level of 0.01 to test the claim that 28% of deaths in the U.S. are caused by heart disease. a. Claim in symbolic form: b. The null hypothesis: c. The alternative hypothesis: d. The type of test (left tailed, right tailed, or two tailed) e. The test statistic (Round to 2 decimal places) f. P-value OR Critical value(s): Label answer as "p-value" or "CV" g. Decision:
Explanation / Answer
a. Claim in symbolic form:
Claim: p = 0.28 [ANSWER]
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b. The null hypothesis:
Ho: p >= 0.28 [ANSWER]
c. The alternative hypothesis:
It is the direct opposite of Ho.
Ha: p < 0.28 [ANSWER]
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d. The type of test (left tailed, right tailed, or two tailed)
As Ha used <, it is LEFT TAILED. [ANSWER]
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e. The test statistic (Round to 2 decimal places)
As we see, the hypothesized po = 0.28
Getting the point estimate of p, p^,
p^ = x / n = 0.2
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.025099801
Getting the z statistic,
z = (p^ - po)/sp = -3.187276292 [ANSWER]
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f)
As this is a 1 tailed test, then, getting the p value,
P value = 0.000718098 [ANSWER]
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g.
As P < 0.01, we REJECT THE NULL HYPOTHESIS.
There is significant evidence at 0.01 level that the percentage of deaths caused by heart disease less than 28%.
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