These numbers are a random sample midterm exam scorefrom 20 students. 65, 50, 75

Question

These numbers are a random sample midterm exam scorefrom 20 students.

65, 50, 75, 70, 68, 58,49, 92, 68, 93, 38, 92, 59, 66, 61, 71, 68,82 ,85 ,67

A) Find the standard error of estimating population mean withsample mean.

B) Provide a point estimate for population standard deviationEMBED Equation.3 ? Is it unbiased?

C) Based on these sample data, if the standard deviation of allstudents’ mid-term score is 1, what is the confidenceinterval for mean mid-term score which we are 90% confidentwith?

D) If we have no information on variance of all students’midterm score, what is the lower confidence bound for mean mid-termscore that we are 99% confident with?

Explanation / Answer

sample size, n = 20 sample mean, x = 68.85 sample standard deviation, s = 14.76 standard error, = s/n = 14.76/20 = 3.3 if standard deviation of all students’ mid-term score is1 standard error, e = 1/20 = 0.224 for 90% confidence, z = 1.65 the confidence interval for mean mid-term score which we are 90%confident with = x ± ze = 68.85 ± (1.65*0.224) = (68.4804, 69.2196) If we have no information on variance of all students’midterm score, the lower confidence bound for mean mid-term score that we are 99%confident with=? for 99% confidence, z = 2.58 hence lower bound = x - ze = 68.85 - (2.58*3.33) = 60.2586

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