Question

test score of all students in Mat 142 classes have a normal distribution. the following is a random sample of 9 test scores from that population :

63, 71, 80, 66, 85, 92, 56, 32, 77

a) determine 95% confidence interval for μ the true mean test score of all Mat142 students( use t-interval procedure)

B) based on the interval you obtained in part a is it likely that μ is 86 or more? explain your answer.

yes or no

reason: ________________________________

Answer 1

a) first we will find the mean and standard deviation of the sample

3969 5041 6400 4356 7225 8464 3136 1024 5929 45544 63 71 80 85 92 32 Sum = 622 The sample mean X is computed as follows 622 9.111 Also, the sample variance s is 6222 45544 319.611 9-1 Therefore, the sample sandartd deviation s is s Vs319.611- 17.878

a) For 95% confidence and df= n-1=8

$T_{\frac{\alpha }{2}}=2.306$

$CI=69.11\pm 2.306(\frac{17.878}{\sqrt{9}})$

$CI=69.11\pm 13.74$

$CI=(55.37,82.85)$

b) No, it is not likely that μ is 86 or more as it is outside the confidence interval calculated above.