Answer: a.) 0.2438 < p < 0.3028
b.) No
Step-by-step explanation: Confidence Interval to estimate the percentage of yellow peas is calculated following these steps:
1) Total of the offspring in one sample:
n = 444 + 167
n = 611
2) Proportion of yellow peas, which is the number of yellow peas observed divided by the total of offspring:
p =
= 0.2733
3) For a 90% confidence interval:
α = 1 - 0.90
Checking z-table, z-score will be: z = 1.645.
4) Calculate margin of error:
E = 0.0295
5) Confidence interval has boundaries:
p - E = 0.2733 - 0.0295 = 0.2438
p + E = 0.2733 + 0.0295 = 0.3028
Then, we are 90% confident that the percentage of yellow peas is between 24.38% and 30.28%.
b.) Since 25% is in the confidence interval, and we are 90% sure the true percentage of yellow peas are inside the interval, the result does not contradict the expectations.