A student is conducting ascience experiment and wants to test whether you would
ID: 2916454 • Letter: A
Question
NUMBER OF HEADS
0
1
2
3
FREQUENCY
53
125
95
27
We are interested in testing whether the coin is fair. One wayto state the null hypothesis is H0: p = .5, where p isthe probability of heads. Use the probabilities in the table belowto determine the expected count of each number of heads in 300repetitions of 3 tosses (use 1 decimal place).
NUMBER OF HEADS
0
1
2
3
PROBABILITY
.125
.375
.375
.125
The conclusion is that we should reject the null hypothesis anddetermine the coin is not fair. Considering this, determinethe value of the standardized residual for each of the categories(don't forget to include the "minus" sign if a standardizedresidual is negative; use 4 decimal places).
1. What is the standardized residual for "0 heads" category? (theanswer is not .94155 or .9416)
2. What is the standardized residual for "1 head" category? (theanswer is not .75932 or .7593)
3. What is the standardized residual for "2 heads" category? (theanswer is not -1.06304 or -1.0630)
4. What is the standardized residual for "3 heads" category? (theanswer is not -.63783 or -.6378)
NUMBER OF HEADS
0
1
2
3
FREQUENCY
53
125
95
27
Explanation / Answer
The formula to calculate the standardized residual in thissituation is (S) = R/SQRT[V(R)]
Here R can be calculated as follows
Number of times headappears
Observed values
Expected values
Residual(R )=Observed-Expected
0
53
37.5
15.5
1
125
112.5
12.5
2
95
112.5
-17.5
3
27
37.5
-10.5
Variance
271
By using the above standardized formula we have the followingvalues
Number of times headappears
Standardizedresidual
0
0.9415
1
0.7593
2
-1.063
3
-0.6378
Number of times headappears
Observed values
Expected values
Residual(R )=Observed-Expected
0
53
37.5
15.5
1
125
112.5
12.5
2
95
112.5
-17.5
3
27
37.5
-10.5
Variance
271
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