Question

A professor is interested in determining how difficult his exams are. He decides to examine past grades on his first exam, the content of which has remained more or less the same over the last several years. In a random sample of 15 exam scores, the sample mean was 75 with a sample standard deviation of 5. The upper bound of a 95% confidence interval for the true mean, to two decimal places, would therefore, be which of the following?

A. 77.77

B. 78.53

C. 77.17

D.73.45

E. 88.85

Answer 1

Solution:

Given that,

n = 15

= 75

s = 5

Note that, Population standard deviation() is unknown. So we use t distribution.

c = 95% = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

Also, d.f = n - 1 = 15 - 1 = 14

    =    =  _0.025,14 = 2.145

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n )

=   2.145 * (5 / 15 )

= 2.77

Now ,

Upper Bound = + E = 75 + 2.77 = 77.77

Answer : 77.77