Problem 2: The average ACT composite score for all applicants to Upper Midwest U

Question

Problem 2: The average ACT composite score for all applicants to Upper Midwest University in 2008 was 23.4. An administrator at UMU wants to know whether the mean ACT composite score of applicants this year is higher. A random sample of 40 UMU applicants in 2014 had a mean of 24.3 with a standard deviation of 2.8. (Don't use Minitab and show your work) a. Identify the parameter of interest above. b. State the hypotheses needed to test whether the mean ACT composite score of UMU applicants is now higher than in 2008. Based on the information above, calculate the appropriate test statistic Find the p-value for this hypothesis test. State a conclusion and interpret the result in terms of this problem at the 5% significance c. d. e. level

Explanation / Answer

a. Here the parameter of interest is "mean of ACT comosite score of for all applicants in Upper midwest University"

b. Here hypothesises are

H0 : ? = 23.4

Ha : ? > 23.4

where ? is the average ACT composite score of UMU

(c) Here sample standard deviation s = 2.8

standard error of sample mean = s/sqrt(n) = 2.8/sqrt(40) = 0.4427

Here test statistic

t = (x? - 23.4)/0.4427 = (24.3 - 23.4)/0.4427 = 2.033

Here dF = 0.05 and dF = 40 - 1 = 39 and one tailed test

tcritical = t39, 0.05 = 1.6849

p - value = 0.0245 [ from softwarre] which is less than 0.05

so here t > tcritical so we will reject the null hypothesis and can conclude that there is significant increase in the average ACT coposite score.

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