Viruses are infectious agents that often cause diseases in plants. Different viruses have different potency levels, and this fact can be used to detect whether a new virus is infecting plants in the field. In a potency comparison experiment, two viruses were placed on a tobacco leaf of 10 randomly selected tobacco plants in a field. The viruses were randomly assigned to one-half of each of the leaves. The table below presents the potency of the viruses, as measured by the number of lesions appearing on the leaf half.
Leaf # 1 2 3 4 5 6 7 8 9 10
Virus X 9 8 3 4 8 4 17 3 14 20
Virus Y 19 8 13 5 16 8 17 6 19 17
Test the hypothesis that there is no difference in mean number of lesions for Virus X and Virus Y
Well, since X has mean 9, and Y has mean 12.8, I'd say it looks bad for the hypothesis.
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To test the hypothesis that there is no difference in the mean number of lesions for Virus X and Virus Y, we can perform a statistical test called the t-test.
Here's how you can do it:
1. Determine the null hypothesis (H0) and alternative hypothesis (Ha):
- Null hypothesis (H0): There is no difference in the mean number of lesions for Virus X and Virus Y.
- Alternative hypothesis (Ha): There is a difference in the mean number of lesions for Virus X and Virus Y.
2. Calculate the means and standard deviations for the two groups:
- Mean for Virus X: Calculated by summing up the values for Virus X and dividing by the number of observations (10 in this case).
- Mean for Virus Y: Calculated by summing up the values for Virus Y and dividing by the number of observations (10 in this case).
- Standard deviation for Virus X: Calculated by using the formula for sample standard deviation.
- Standard deviation for Virus Y: Calculated by using the formula for sample standard deviation.
3. Perform the t-test:
- The t-test allows us to determine if the difference in means between two groups is statistically significant.
- There are different types of t-tests, but in this case, we can use an independent samples t-test since the two groups (Virus X and Virus Y) are independent of each other.
- The t-test will calculate a t-value and a p-value.
4. Calculate the t-value and p-value:
- The t-value is calculated using the means, standard deviations, and sample sizes of the two groups.
- The p-value represents the probability of obtaining the observed data if the null hypothesis (H0) is true.
- The p-value will help determine if the observed difference in means is statistically significant or due to random chance.
5. Determine the significance level:
- Choose a significance level (alpha) to determine the threshold for acceptance or rejection of the null hypothesis.
- Common significance levels include 0.05 (5%) and 0.01 (1%).
6. Compare the p-value to the significance level:
- If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference in the mean number of lesions for Virus X and Virus Y.
- If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in the mean number of lesions for Virus X and Virus Y.
By following these steps and calculating the appropriate values, you can test the hypothesis and determine if there is a significant difference in the mean number of lesions for Virus X and Virus Y.