Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 442 green peas and 171 yellow peas. a. Construct a 95​% confidence interval to estimate of the percentage of yellow peas. b. It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations? a. Construct a 95​% confidence interval. Express the percentages in decimal form. nothingless thanpless than nothing ​(Round to three decimal places as​ needed.) b. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

Answer 1

Solution:

Given: A genetic experiment with peas resulted in one sample of offspring that consisted of 442 green peas and 171 yellow peas.

Thus sample size = n = 442 + 171 = 613

x = number of yellow peas = 171

c = confidence level = 95%

Part a) Construct a 95​% confidence interval to estimate of the percentage of yellow peas.

Formula:

where

and

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus

Thus a 95​% confidence interval to estimate of the percentage of yellow peas is between :

Part b) It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

No. Since a 95​% confidence interval to estimate of the percentage of yellow peas include expected percentage of offspring yellow peas = 25% =0.25.