Question

1. This problem is the check to see whether you understand the X-squared test. There are only 2 test columns, so you cannot use the X-squared Goodness of Fit applet from the previous problem as it requires 3 or more test intervals.

You are told that a genetics theory says the ratio of tall:short plants is 3:1. You test this claim by growing 200 plants. You obtain 160 tall plants and 40 short plants. Using a X-squared test, determine whether or not your results supports the tall:short = 3:1 claim.

1. What is the null hypothesis for this test?
2. What is the alternative hypothesis?
3. Fill in the following table.

Card Color	Observed	Expected	(O – E)	(O-E)2	(O-E)2/E
Red	160
Black	40
Sum	200	200	0	n/a

4. What is the value of X² for this data?
5. What is the number of degrees of freedom?
6. Use the X² calculator to compute p (use the right tail option). Provide a screen shot of your calculation.

7. Does this value of p support the null hypothesis at the 10% significance level? (yes or no and explain using your numbers)

Answer 1

H0 : Results supports the tall:short = 3:1 claim

H1 : Results does not support the tall:short = 3:1 claim

Card Color	Observed	Expected	(O – E)	(O-E)2	(O-E)2/E
Red	160	150	10	100	0.666667
Black	40	50	-10	100	2
Sum	200	200	0	n/a	2.666667

value of X² = 2.666667

degrees of freedom = n-1 = 1

Yes, the value of p support the null hypothesis at the 10% significance level because P-value = 0.4142 >0.10, we fail to reject H0.