Question

14.

A genetic experiment with peas resulted in one sample of offspring that consisted of 433 green peas and 153 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?

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a. Construct a 95​% confidence interval. Express the percentages in decimal form.

<p< (Round to three decimal places as​ needed.)

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b. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

​Yes, the confidence interval does not include​ 0.25, so the true percentage could not equal​ 25%

​No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%

Answer 1

Solution :

Given that,

a) n = 433 + 153 = 586

x = 153

Point estimate = sample proportion = = x / n = 153 / 586 = 0.261

1 - = 1 - 0.261 = 0.739

Z/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.261 * 0.739) / 586)

= 0.036

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.261 - 0.036 < p < 0.261 + 0.036

( 0.225 < p < 0.297 )

b) ​No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%