Question

- 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.

- What is the null hypothesis for this test?
- What is the alternative hypothesis?
- Fill in the following table.

Card Color |
Observed |
Expected |
(O – E) |
(O-E) |
(O-E) |

Red |
160 |
||||

Black |
40 |
||||

Sum |
200 |
200 |
0 |
n/a |

- What is the value of X
^{2}for this data? - What is the number of degrees of freedom?
- Use the X
^{2}calculator to compute p (use the right tail option). Provide a screen shot of your calculation.

- 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 X^{2} = 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.

3. 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...

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