Question

A statistics instructor wishes to estimate the mean SAT score in his state this year. A sample of 595 exams in his state have an average score 470. It is known that SAT scores are normally distributed with a standard deviation of 100. Based on his sample, construct a 98% confidence interval for all SAT scores in his state.

Answer 1

Formula for Confidence Interval for population Mean When Population Standard deviation is known

for 98 % confidence level = (100-98)/100 =0.02

/2 = 0.02/2 =0.01

Z/2 = Z0.01 = 2.3263

Number of exams in the sample: Sample size : n= 595

Sample average score : Sample average : = 470

SAT scores are normally distributed with a standard deviation of 100 i.e Population standard deviation : =100

98% confidence interval for all SAT scores in his state

98% confidence interval for all SAT scores in his state = (460.4631,479.5369)