please help me !

Question

An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. If at the end of the semester she has the following grades was she correct in her hypothesis? Use α = 0.05 . A B C D F 6 14 22 8 4

Answer 1

So 6 grades of A

  14 grades of B

  22 grades of C

  8 grades of D

  4 grades of F.

 

Looks like a decent bell curve to me..... ;-)

THere are 54 students that tested, per the total.

 

6/54 = 1/9 = 0.111.... = 11.1% for the A's

 

14/54 = 7/27 = 0.259259259259.... = 25.925% for the B's

 

 22/54 = 11/27 = 0.407407407... = 40.740% for the C's

 

8/54 = 4/27 = 0.148148148148... = 14.814% for the D's

 

4/54 = 2/27 = 0.074074074074.... = 7.407% for the F's

 

 

Now it's time for the Chi-Square test (Goodness of Fit). The formula is:

 

 sum of  (observed - expected)^2/ expected)

 

Here's the table that calculates it, courtesy of MS Excel:

Observed          Expected     (Obs - exp)             (obs -exp)^2      chi-square
0.111111             0.1            0.011111            0.000123454         0.001234543
0.259259259       0.23          0.029259259       0.000856104         0.003722192
0.407407407       0.45          -0.042592593       0.001814129        0.004031398
0.148148148       0.14            0.008148148        6.63923E-05       0.000474231
0.74074074         0.08            0.66074074           0.436578325     5.457229069

                                                                       TOTAL IS ---->  5 .466691433

 

 

Examining the Chi Square table, with 5% confidence, the test statistic is well

within range for any number of degrees of freedom greater than 1. In this

problem, there are in fact 54 df.

 

So yes, there is statistical evidence that supports the claim.