Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean p. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 76 and the standard deviation was 7.7, construct a 99% confidence interval for the mean score of all students. 72.13 < x < 79.87 73.61 < p < 78.39 O 72.54 < p < 79.46 O 72.14< p < 79.89

Answer 1

Solution:

Given:

Sample mean = = 76

r

Sample sd = s = 7.7

Sample size = n = 30

Degrees of freedom = df = n-1 = 30-1 = 29

Level of significance = α=0.01

Critical t = 2.756 ..Using excel formula  =TINV(0.01,29)

The 99% confidence for the population mean μ is

te x 8 * X + te x 8 n n

2.756 x 7.7 76 - 76 + 2.756 x 7.7 30 V30 = (76 – 3.875, 76 +3.875)

= (72.13 , 79.87)

Hence, 99% confidence for the population mean μ is 72.13 < μ < 79.87

Done