Question
he University of the Free State wishes to investigate if a new variety of wheat is more susceptible to a disease that an old variety. It is known that this disease strikes approximately 15% of all wheat plants. A field experiment was conducted, and of 120 new plants, 90 become infected. The null and alternative hypothesis is:
Answers
GPT-4o mini
In this scenario, you can formulate your null and alternative hypotheses as follows:
- **Null Hypothesis (H0)**: The new variety of wheat is not more susceptible to the disease than the old variety. This can be interpreted as the proportion of infected plants in the new variety is equal to the known disease strike rate of 15%. Mathematically, this can be stated as:
\[
p = 0.15
\]
- **Alternative Hypothesis (H1)**: The new variety of wheat is more susceptible to the disease than the old variety. This can be interpreted as the proportion of infected plants in the new variety is greater than 15%. Mathematically, this can be stated as:
\[
p > 0.15
\]
Where \( p \) is the proportion of infected plants in the new variety of wheat.
Given that out of 120 new plants, 90 became infected, you can also calculate the sample proportion \( \hat{p} \) for the new variety:
\[
\hat{p} = \frac{90}{120} = 0.75
\]
You can then conduct a hypothesis test (such as a z-test for proportions) to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
- **Null Hypothesis (H0)**: The new variety of wheat is not more susceptible to the disease than the old variety. This can be interpreted as the proportion of infected plants in the new variety is equal to the known disease strike rate of 15%. Mathematically, this can be stated as:
\[
p = 0.15
\]
- **Alternative Hypothesis (H1)**: The new variety of wheat is more susceptible to the disease than the old variety. This can be interpreted as the proportion of infected plants in the new variety is greater than 15%. Mathematically, this can be stated as:
\[
p > 0.15
\]
Where \( p \) is the proportion of infected plants in the new variety of wheat.
Given that out of 120 new plants, 90 became infected, you can also calculate the sample proportion \( \hat{p} \) for the new variety:
\[
\hat{p} = \frac{90}{120} = 0.75
\]
You can then conduct a hypothesis test (such as a z-test for proportions) to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.