Formula:   Chi-Square = S [ (Observed_i - Expected_i)² / Expected_i ]

The larger that the value of Chi-Square is the more deviation there is from what is expected.

In the following exercises, if no statement to the contrary is made, use the 5% level of significance.  Also use one-decimal accuracy for expected values.  Note:  The number of degrees of freedom (df) for a contingency table is  df = (rows - 1)(columns - 1).  The number of degrees of freedom for a list of n observations is    df = n - 1.
 

1.  A die is tossed 100 times and the following results are obtained.
 

Face	1	2	3	4	5	6
Observed	12	17	20	22	13	16

Determine whether this die could still be considered honest on the basis of the 1% level of significance.
 

2.  In a cross between ivory and red snapdragons the following counts are observed in the second generation.
 

Color	Red	Pink	Ivory
Number of Plants	20	55	25

On the basis of these data, can segregation be assumed to occur according to the simple Mendelian ratio 1:2:1?
 

3.  In an experiment involving crossing two hybrids of a species of flower the results shown below are observed.  Are these results consistent with the expected proportion 9:3:3:1?
 

	Green Stigma	Red Stigma
Magenta Flower	120	49
Red Flower	36	12

 

4.  Of 64 offspring of a certain cross between guinea pigs, 34 are red, 10 are black, and 20 are white.  According to the genetic model, these numbers should be in the ratio 9:3:4.  Are the data consistent with the model?
 

5.  According to the genetic model, offspring of a certain cross between guinea pigs are red, black, or white in the ratio 9:3:4.  A worker wishing to disprove this theory for a particular experiment has reason to believe that the offspring will occur in the ratio 8:5:3.  If in this experiment the results occur precisely in the ratio 8:5:3, how many offspring must there be in the sample in order that the worker can be 95% confident he has disproved the hypothesis of a 9:3:4 ratio?
 

6.  In a random sample of 1000 housewives 55% state a preference for brand A and 45% for brand B.  Is this result compatible with the hypotheses that 50% of all housewives prefer brand A?
 

7.  Fifty individuals are classified according to eye color and shade of hair.  Can we conclude from the data shown below that for these individuals there is a significant connection between eye color and hair shade?
 

	Light Hair	Dark Hair
Blue Eyes	23	7
Brown Eyes	4	16

 

8.  In three groups of people, chosen from different geographical regions, the distribution of hair color is as follows.  Do these data indicate that hair color is dependent on geographical region?  (Use the 2% level of significance.)
 

	Red Hair	Light Hair	Dark Hair
Group A	2	9	9
Group B	3	6	21
Group C	15	15	20

 

9.  Analyse your individual M&M data to see whether your data is significantly different from expected.  You will need to refer to the percentages given by Mars listed in the M&M project questions.
 

ANSWERS