Unprotected skin cells mutate at a rate of 20% when exposed to 10 rads of UV radiation. A group of scientists tested whether Sun Screen X will decrease the mutation rate. 1100 cells were tested, exposed and counted. Only 200 cells had mutated, 900 cells remained unchanged. What is the x^2 number that would be calculated from this data using the null hypothesis that "sun screen X results in no significant change"?
If someone could show me how to start this problem, that'd be great. Thanks
To calculate the chi-square (χ²) value, you will need to set up a contingency table with the observed and expected frequencies based on the null hypothesis.
The expected frequency is the number of cells that would be expected to mutate based on the assumption that there is no significant change caused by Sun Screen X. The null hypothesis states that there is no significant difference between the mutation rate with and without Sun Screen X.
Let's set up the contingency table:
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| Mutated Cells | Non-mutated Cells |
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Observed Frequencies | 200 | 900 |
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Expected Frequencies | ? | ? |
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To calculate the expected frequencies, we need to use the mutation rate of 20% and the total count of cells (1100).
- For the mutated cells, the expected frequency can be calculated as 20% of the total cell count: 0.2 * 1100 = 220.
- For the non-mutated cells, the expected frequency can be calculated as the remaining count: 1100 - 220 = 880.
Now that we have the expected frequencies, we can fill in the contingency table:
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| Mutated Cells | Non-mutated Cells |
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Observed Frequencies | 200 | 900 |
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Expected Frequencies | 220 | 880 |
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Next, we can calculate the chi-square value using the formula:
χ² = Σ((O - E)² / E)
where Σ represents the summation, O is the observed frequency, and E is the expected frequency.
Calculating for the mutated cells:
χ² = ((200 - 220)² / 220)
Calculating for the non-mutated cells:
χ² = ((900 - 880)² / 880)
Finally, sum up the two calculated values:
χ² = ((200 - 220)² / 220) + ((900 - 880)² / 880)
This will give you the chi-square value for your data under the null hypothesis that Sun Screen X results in no significant change.