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Part 1
In an experiment on chlorophyll inheritance in​ corn, for 1098 seedlings of​ self-fertilized heterozygous green​ plants, 849 seedlings were green and 249 were yellow. Theory predicts that​ 75% of the seedlings would be green
Report the​ P-value.
​P-valueequals
  
enter your response here ​(Round to the nearest hundredth as​ needed.)

To find the p-value, we need to perform a hypothesis test for proportions. Here, the null hypothesis is that the proportion of green seedlings is \(75\%\) (or \(0.75\)).

### Step 1: Set Up the Hypotheses

- Null Hypothesis (\(H_0\)): The proportion of green seedlings \(p = 0.75\).
- Alternative Hypothesis (\(H_a\)): The proportion of green seedlings \(p \neq 0.75\).

### Step 2: Calculate the Sample Proportion

The sample proportion \(\hat{p}\) is calculated as:

\[
\hat{p} = \frac{\text{Number of green seedlings}}{\text{Total number of seedlings}} = \frac{849}{1098} \approx 0.7732
\]

### Step 3: Calculate the Standard Error (SE)

The standard error for the sample proportion is:

\[
SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.75 \times (1 - 0.75)}{1098}} = \sqrt{\frac{0.75 \times 0.25}{1098}} \approx \sqrt{\frac{0.1875}{1098}} \approx 0.0129
\]

### Step 4: Calculate the Z-Score

The z-score is calculated as:

\[
z = \frac{\hat{p} - p}{SE} = \frac{0.7732 - 0.75}{0.0129} \approx \frac{0.0232}{0.0129} \approx 1.80
\]

### Step 5: Find the P-Value

The p-value corresponds to the area under the normal distribution curve beyond the calculated z-score, which can be found using standard normal distribution tables or software.

For a two-tailed test:

- Look up the p-value for \(z = 1.80\).

Using a z-table or calculator, the p-value for \(z = 1.80\) is approximately \(0.0359\) for one tail. Since it's a two-tailed test, multiply by 2:

\[
\text{P-value} \approx 2 \times 0.0359 = 0.0718
\]

### Final Answer:

The p-value is approximately **0.07** (rounded to the nearest hundredth).

Would you like any further details or explanations?

Here are some related questions:

1. How do you interpret the p-value in this context?
2. What would your conclusion be if the p-value were below 0.05?
3. How does the sample size affect the standard error and p-value?
4. What is the meaning of the z-score in this test?
5. How would you calculate the p-value for a one-tailed test in this scenario?
6. What is the difference between the p-value approach and the critical value approach in hypothesis testing?
7. How could the results change if the predicted proportion was different?
8. What assumptions must be met to use this z-test for proportions?

**Tip**: Always check whether your test is one-tailed or two-tailed when interpreting p-values to avoid incorrect conclusions.

Learn how to calculate the p-value for a hypothesis test on chlorophyll inheritance in corn using statistics. This problem involves determining whether the observed proportion of green seedlings matches the theoretical prediction. Understand the steps involved in hypothesis testing, including calculating sample proportions, standard errors, and z-scores. Suitable for advanced high school and college students.

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