A teacher figures that final grades in the statistic department are distributed

Question

A teacher figures that final grades in the statistic department are distributed as: A, 20%; B, 30%; c, 40%; D, 6%; F, 4%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic chi^2 to determine if the grade distribution for the department is different then expected. (a) Find the margin of error for the given values of c, sigma, and n. c = 0.99, sigma = 10, n = 10 (b) A random sample of 140 students has a grade point average with a mean of 2.73. Assume the population standard deviation is 0.75. Construct the confidence interval for the population mean, mu, if c = 0.95.

Explanation / Answer

for 0.05 level of significnace critical value =9.4877

as chi stat is lower then crtiical value we can not reject that it follows given distribution,

 a) for c=0.99, z=2.5758

and std error =std deviation/(n)1/2 =0.9535

hence margin of error =z*std error = 2.456

3) std error=std deviation/(n)1/2 =0.0634

for c=0.95 ; z=1.96

hence confidence interval =sample mean -/+ z*std error =2.6058 ; 2.8542

observed Expected Chi square Grade Probability O E=total*p =(O-E)^2/E A 0.200 40.000 31.60 2.23 B 0.300 36.000 47.40 2.74 C 0.400 60.000 63.20 0.16 D 0.060 14.000 9.48 2.16 F 0.040 8.000 6.32 0.45 1 158 158 7.7384

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