Question

A Genetic experiment with peas resulted in one sample of offspring that consisted of 430 green peas and 159 yellow peas.

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

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B) Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

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

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

Answer 1

Solution :

Given that,

n = 430

x = 159

= x / n = 159 / 430 = 0.370

1 - = 1 - 0.370 = 0.630

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.370 * 0.630) / 430)

= 0.046

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.370 - 0.046 < p < 0.370 + 0.046

0.324 < p < 0.416

B)

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