A sample of 20 students take Math 203 was randomly selected to evaluate the resu

Question

A sample of 20 students take Math 203 was randomly selected to evaluate the results on the Math 203 final tes. The average for the sample was 74 with a standard deviation of 7.5. Determine the 95% confidence interval for students taking the test. Previous studies indicate a standard deviation of 8.3. (Assume that the population standard deviation is the 8.3.) Assume the population is approximately normally distributed.

Directions

Answer the following:
1. Determine the type of confidence interval (z, t, or proportion).
2. State the confidence interval. Round your answer to 1 decimal place.
3. Based on your confidence interval for the population (true) mean, do you feel the average is too low and the test needs to be changed? Explain your answer

Explanation / Answer

1) as we know the population std deviation type of confidence interval : z

2) for std error of mean =std deviation/(n)1/2 =1.677

for 95% confidence interval ; z=1.96

hence 95% confidence interval =sample mean -/+ z*std error =74 -/+ 1.96*1.677 =70.7 ; 77.3

3)The average does not seem to be too low as it lies in between of 3rd and 4th quartile, therefore we are not requird to change the test.

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