Pregunta
A genetic experiment with peas resulted in one sample of offspring that consisted of 442 green peas and 152 yellow peas.
a. Construct a
confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that
of the offspring peas would be
a. Construct a
confidence interval. Express the percentages in decimal form.
(Round to three decimal places as needed.)
a. Construct a
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that
a. Construct a
Ask by Estrada Ingram. in the United States
Mar 15,2025
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Respuesta verificada por el tutor
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a. The
confidence interval for the percentage of yellow peas is
.
b. The expected
of yellow peas falls within the confidence interval, so the results do not contradict the expectation.
Solución

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Como
Bonus Knowledge
To construct a 95% confidence interval for the percentage of yellow peas, we first need to calculate the sample proportion of yellow peas.
The total number of peas is
. The proportion of yellow peas (
) is given by:
Next, we calculate the standard error (SE) using the formula:
Now, for a 95% confidence interval, we use a z-score of approximately 1.96. The confidence interval is calculated as:
Calculating this gives us:
Therefore, the confidence interval for the proportion of yellow peas is:
So, expressed in the requested format:
(Rounded to three decimal places as needed.)
Based on this confidence interval, we can see that the lower bound (0.217) is significantly above the expected percentage of yellow peas (0.25), suggesting that the experimental results do not contradict the expectation. In fact, with this data, we find that there’s a considerable chance that yellow peas could represent around 25.6% to 29.5% of the offspring, aligning relatively well with the expectation.

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