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A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 163 yellow peas. a. Construct a 95% 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 25% of the offspring peas would be yellow? a. Construct a 95% confidence interval. Express the percentages in decimal form. square lt plt square (Round to three decimal places as needed.)

Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 163 yellow
peas.
a. Construct a 95%  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 25%  of
the offspring peas would be yellow?
a. Construct a 95%  confidence interval. Express the percentages in decimal form.
square lt plt square  (Round to three decimal places as needed.)

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 163 yellow peas. a. Construct a 95% 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 25% of the offspring peas would be yellow? a. Construct a 95% confidence interval. Express the percentages in decimal form. square lt plt square (Round to three decimal places as needed.)

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JuddProfessional · Tutor for 6 years

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a. The 95% confidence interval is \( 0.241 < p < 0.307 \) (rounded to three decimal places)<br />b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow. This is because 0.25 does not fall within the calculated confidence interval \( 0.241 < p < 0.307 \). This suggests that the yellow peas do not follow Mendelian genetics relevant for the spacing of the two types of peas in future generations as per the given data.

Explain

## Step1<br />First, we need to calculate the sample proportion (p). The sample proportion is the ratio of the number of successes (yellow peas) to the total number of trials (total peas).<br /><br />### \( p = \frac{x}{n} = \frac{163}{595} \approx 0.274 \)<br /><br />## Step2<br />The conditions for constructing a confidence interval are:<br />1. The product of the sample size and the sample proportion (np) and the product of the sample size and the sample proportion (1-p) should both be greater than 5.<br />2. The sample is less than 10% of the population.<br /><br />In our case, both conditions are met.<br /><br />## Step3<br />We can now construct the confidence interval using the formula:<br /><br />### \( CI = p \pm Z \sqrt{\frac{p(1-p)}{n}} \)<br /><br />Where Z is the Z-value from the standard normal distribution for the desired confidence level.<br /><br />## Step4<br />Substituting the given values into the formula, we get:<br /><br />### \( CI = 0.274 \pm 1.96 \sqrt{\frac{0.274(1-0.274)}{595}} \)<br /><br />## Step5<br />Calculating the above expression gives us the confidence interval.<br /><br />## Step6<br />Finally, we compare the calculated confidence interval with the expected proportion of 25% (or 0.25). If 0.25 falls within the calculated confidence interval, then the results do not contradict the expectation. If not, they do contradict the expectation.
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