Question

10) The SAT scores for 12 randomly selected seniors at a particular high school are given below. Assume that the SAT scores for seniors at this high school are normally distributed.

1,099	678	690	873	721	651
689	790	1,150	754	709	686

a) Find a 95% confidence interval for the true mean SAT score for students at this high school.

b) Provide the margin of error of the interval as your answer.

Round your answer to the nearest whole number.

Answer 1

Q.10) sample size (n) = 12

Using Excel we get, sample mean = 790.8333

and sample standard deviation (s) = 167.1857

a) t-critical value at significance level of 0.05 with degrees of freedom = 12 - 1 = 11 is,

Excel Command : = TINV(0.05, 11) = 2.201

The 95% confidence interval for the population mean is,

Therefore, the 95% confidence interval for the true mean SAT score for students at this high school is (685, 897).

b) The margin of error (E) is,

Therefore, required margin of error is 106