The average ACT composite score for all applicants to Upper Midwest University i

Question

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 15 UMU applicants in 2014 had a mean of 24.3 with a standard deviation of 2.8. Assume the ACT composite score for all applicants to Upper Midwest University in 2008 has Normal distribution. 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. c) Based on the information above, calculate the appropriate test statistic. d) Find the p-value for this hypothesis test. e) Interpret and state a conclusion in terms of this problem at the 5% significance level.

Explanation / Answer

a) x = 24.3 , s = 2.8 , n = 15 , mean = 23.4

b)

Hypothesis:

H0; mu = 23.4

Ha: mu > 23.4

c) t = ( x - mean) / ( s /sqrt(n))

= ( 24.3 - 23.4) / ( 2.8 / sqrt(15))

= 1.25

d)

p value using t = 1.28 , df = 14

P value = .110675.

e) As p value is less than 0.05 So, we fail to reject the null hypothesis.

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