Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 431 green peas and 152 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 pets 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 << (Round to three decimal places as needed.) b. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations? O No, the confidenqe interval includes 0.25, so the true percentage could easily equal 25% Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%

Answer 1

Solution:

Given:

Green peas = 431

Yellow Peas = 152

thus n = 431 + 152 = 583

Part a) Construct a 95% confidence interval .

Formula:

(-E <p< p + E)

where

2 = 0.2607

and

E = Z X P * (1-P)

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.

17 .00 .01 .02 ,03 ,04 ,05 06 .07 .08 .09 | 0.0 5000 15040 .5080 5120 .5160 5199 5139 5279 5319 .5359 10.1 .5398 5438 .5478 .5517 .5557 5596 .56 36 .5675 714 .5753 10.2 5793 ,5832 .5871 .5910 .5948 .5987 .6126 16064 .6103 .6141 10.3 .6179 .6217 .6255 .6293 6331 .6368 .6-06 .6443 .6480 .6517 10.4 .6554 ,6591 .6628 .6664 ,6700 .6736 | 672 .6808 .684 6879 10.5 46915 .6950 .6985 7019 7054 088 H23 71771907224 | 0.6 .72772917324 137 .7389 7422 7454 74867517 7549 107,750761176427673704734 TEA T97823 7852 10. 8 79617910793979677995.8023 80518078,8106 18133 10.9 .8159 .8186 8212 18238 1.8264 1.8289 8315 8340 18365 18292 1.0 .8413 8438 .8461 .8485 85088531 8554 .85 ,8599 18621 1. 1 6 43 ,8665 ,8686 8708 8729 8749 80 8790,8810 1.8830 1.2 .88988698888 8907925 .8948862 ,8980 .8997 9015 13 032 9049 9066 190829099_9115 913191479162 9177 11. 491929207922292369251 9265 99 9292 9306 19319 11.5 9332 9345 .9357 19370 19382 9394 9406 9418 19429 19441 11.6 94529463 .9474 9484 1.9495 9505 15 19525 .9535 19545 | 1.7 .9554 19564 9573 19582 9591 9599 508 19616 9625 19633 11.8 195419649 19656966496719678 +86 9693 ,9699 19706 | 1.9 -7139719 972673278 74,9750 9756 19761 19767

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

That is : Z_c = 1.96

thus

E = Z X P * (1-P)

E = 1.96 x 0.2607 x (1 – 0.2607) 583

E = 1.96 V 0.2607 x 0.7393 583

E = 1.96 X V0.00033061

E = 1.96 x 0.0181827

E = 0,035638

thus

(-E <p< p + E)

(0.2607 – 0.035638 <p < 0.2607 + 0.035638)

(0.225082 <p < 0.296358)

(0.225 <p < 0.296)

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