Question

# This problem is the check to see whether you understand the X-squared test. There are only...

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

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

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.

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