According to the Association of American Medical Colleges, 46% of all medical sc

Question

According to the Association of American Medical Colleges, 46% of all medical school applicants were admitted to medical school in the fall of 2011. After reading this publication, the trustees at a particular college voiced their concern to the college president since only 72 of the 180 students in the school's class of 2011 who applied to medical school were admitted. The college president reassured the board that their success rate was consistent with the national average; that is, the fluctuation in year-to-year acceptance is to be expected. Assume the college's applicants to medical school for 2011 are a representative sample of all medical school applicants from the college each year. The following questions are regarding the estimation of the population proportion, p, referenced in the scenario above, at the 95% confidence level: The following questions are regarding the test of the population proportion, p, referenced in the scenario above, to determine if the rate of acceptance to medical school for the college is inconsistent with the national average. a. What are the appropriate null and alternative hypotheses for the test of pi Is this a left-tailed (lowertailed), right-tailed (upper-tailed) or two-tailed test? b. At the 5% significance level, use the P-value approach to determine if the data provides sufficient evidence that the rate of acceptance to medical school for the college differs from the stated national average of 46%. Explain how you made your decision and state your conclusion in the context of the problem (scenario). c. Instead of using the P-value to determine if the sample data provides sufficient evidence to reject the null hypothesis, we could use a confidence interval estimate constructed with the same sample data and confidence level that equals 1 -alpha. If the hypothesized [true] value of the parameter is within the limits of the confidence interval, it is considered plausible and we consequently fail to reject the null hypothesis.

Explanation / Answer

Excel formula:

given p0= 0.42 p= 0.4 n= 180 std error= 0.036788 a) This is z-proportion 2 tailed test since with following hypothesis: H0: p=p0 Ha: p not equal p0 b) hypothesis testing: z= 0.54366 p-value= p-value>.05; we cant reject H0 & we conclude that p is equal to p0 c) we will compute 95% confidence interval upeer bound= 0.472103 lower bound= 0.327897 since 0.42 is in the above limit so conclusion remains same.

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