Please help me solve this by showing the formulas to find the solutions, your wo
ID: 3062658 • Letter: P
Question
Please help me solve this by showing the formulas to find the solutions, your work and on paper. A picture of the work on paper will suffice, thank you!
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According to the American Diabetes Association (www.diabetes.org), 23.1% of Americans aged 60 years or older had diabetes in 2007. A recent random sample of 200 Americans aged 60 years or older showed that 52 of them have diabetes. Using 5% significance level, perform a test of hypothesis to determine if the current percentage of Americans aged 60% or older who have diabetes is higher than 23.1%
Ho_____________________________; H1______________________________
(proportional to)=_____________________________
Critical value or p-value__________________________________________________
Conclusion____________________________________________________________
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.231
Alternative hypothesis: P > 0.231
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.0298
z = (p - P) /
z = 0.973
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 greater than 0.973.
Thus, the P-value = 0.1587
Interpret results. Since the P-value (0.1587) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that current percentage of Americans aged 60% or older who have diabetes is higher than 23.1%.