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.)
Answer
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Judd
Professional · Tutor for 6 years
Answer
a. The 95% confidence interval is
(rounded to three decimal places)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
. 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.
Explanation
## Step1First, 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).###
## Step2The conditions for constructing a confidence interval are: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 5.2. The sample is less than 10% of the population.In our case, both conditions are met.## Step3We can now construct the confidence interval using the formula:### \( CI = p \pm Z \sqrt{\frac{p(1-p)}{n}} \)Where Z is the Z-value from the standard normal distribution for the desired confidence level.## Step4Substituting the given values into the formula, we get:### \( CI = 0.274 \pm 1.96 \sqrt{\frac{0.274(1-0.274)}{595}} \)## Step5Calculating the above expression gives us the confidence interval.## Step6Finally, 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.