Part A
There are 166 yellow out of 448+166 = 614 total.
phat = sample proportion of yellow peas
phat = 166/614
phat = 0.270358 approximately
At 95% confidence, the z critical value is roughly z = 1.960; use a stats table or stats calculator to determine this.
Let's calculate the margin of error.
E = z*sqrt(phat*(1-phat)/n)
E = 1.960*sqrt(0.270358*(1-0.270358)/614)
E = 0.035131 approximately
Now we can compute the lower and upper boundaries (L and U)
L = lower boundary
L = phat - E
L = 0.270358 - 0.035131
L = 0.235227
L = 0.235
and
U = upper boundary
U = phat + E
U = 0.270358 + 0.035131
U = 0.305489
U = 0.305
The 95% confidence interval of the form L < p < U is roughly 0.235 < p < 0.305
That condenses to (0.235, 0.305)
We are 95% confident the true population proportion (p) is somewhere between 0.235 and 0.305
Answer: The 95% confidence interval is approximately (0.235, 0.305)
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Part B
25% converts to the decimal form 0.25 or 0.250
Since 0.250 is between 0.235 and 0.305, i.e. 0.235 < 0.250 < 0.305 is true, this means that it is possible that p = 0.250 is the case.
Therefore, it is possible that roughly 25% of the offspring peas are yellow.
Answer: The results of the experiment do not appear to contradict the expectation of 25% yellow.