Name ________________________
                                                       (5 points)

1. (20 points) The Student Affairs Office at a local university is
studying the mathematics skills of incoming freshmen. A random sample
of 30 new freshmen was selected and studied. The mathematics ACT scores
for the members of the sample were obtained and are displayed in the stem
and leaf diagram below.

1f  5 5                                   a) Find the five number summary
1s  6 6 7                                    and sketch box plot.
1*  9 9 9
2   0 0 0 0 1 1 1
2t  2 2 2 2 3                             b) Given that S x = 656
2f  4 4 5                                    S x2 = 14,846, compute the mean,
2s  6 6 6 7 7                                variance and standard deviation.
2*
3   0 1
 

2. (20 points) How large are the high school graduating classes that Millikin
freshmen come from? A random sample of 15 current freshmen was selected and
the size of their graduating class was obtained. The graduating class sizes were:

35 53 351 233 226 154 33 102 149 502 241 284 82 149 72

a) Estimate the mean graduating class size with a 95% confidence interval.

b) Estimate the graduating class size for the center 95% of the entering
freshmen class. Interpret your interval.

c) If the estimate should be accurate to within 20 students, how large
should the sample be?

3. (10 points) A nearby competing university has advertised that their mean
ACT composite ACT score for incoming freshmen is 22. A random sample of 147
Decatur University entering freshmen had a mean ACT composite score of 22.39
with standard deviation 3.71. Is there evidence to indicate that the mean
ACT composite score for Decatur University entering freshmen is higher
than 22, the mean for the nearby university? Find the p-value of the test.

4. (25 points) Did the male entering freshmen at Decatur University do as
well as the female entering freshmen? Random samples of 50 entering
females and 43 entering males were selected to help answer this question.
The percentile of each sample members high school gpa (within their
respective high school graduating class) was obtained.

a) Is there evidence to indicate that the mean gpa percentiles for male
and female entering students are not equal? Test using a = 0.04.

male         female

n_m = 43      n_f = 50
_            _
x_m = 64.6    x_f = 73.3

s_m = 19.6    s_f = 17.7
 

b) Estimate the difference in mean gpa percentile with a 90% confidence interval.
 
 

6. (20 points) Do standardized tests really predict success in college?
The Mathematics Department at Decatur University is wondering whether
the math ACT score will predict success in Calculus I. A random sample
of 40 recent Calculus I students was selected. The math ACT scores (x)
and the grades in Calculus I (y), on a 4 point scale, were obtained for
the 40 members of the sample. Some preliminary calculations on the
data are reported below.
 

a) Use the sample to predict the Calculus I grade of a student who
   had 24 on the math ACT.

b) Test the hypothesis that the slope of the least squares line of best
   fit is not 0 using a = 0.05.
 
         S x = 1028     S x² = 27,064    SS_xx = 644.4

        S y = 97       S y² = 289.32     SS_xy = 97.6

     S xy = 2,590.5     n = 40         SS_yy = 54.095

_{L                   L}
b₁ = 0.151459       b₀ = -1.467489