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.

867	1,234	894	1,264	614	861
1,382	968	824	944	702	1,360

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

a)

Sample mean = X / n = 992.83

Standard deviation S = sqrt [ X² - n ² / n -1 ] = 255.9371

df = n - 1 = 12 - 1 = 11

t critical value at 0.05 significance level with 11 df = 2.201

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

992.83 - 2.201 * 255.9371 / sqrt(12) < < 992.83 + 2.201 * 255.9371 / sqrt(12)

830.21 < < 1155.45

95% C I is ( 830 , 1155 )

b)

Margin of error E =  t * S / sqrt(n)

= 2.201 * 255.9371 / sqrt(12)

= 163