Question

Show vour work. Show symboic formulas when Gregor Mendel conducted his famous genetics experiments with peas. one sample of offspring consisted of 445 green peas and 156 yellow peas. Find a 90% confidence interval estimate of the population proportion of green peas. a) Critical value = Explain which distribution that you chose. four decimals Margin of error, E= b) three decimals <p< Confidence Interval: c) u Tdte Give three possible values of the population proportion p (three decimals). d) Does the result contradict the claim that 75 % of peas are green? Explain. e)

show all work and formulas

Answer 1

(a)

$\alpha$ = 0.10

From Table:

Critical value = $\pm$1.645

Z Distribution because of Large Sample, n > 30

(b)

Green peas = 445

Yellow peas = 156

Total peas = 601

Sample Proportion of Green peas = $\hat{p}$ = 445/601 = 0.7404

n = Sample Size = 801

$\hat{q}$ = 1 - $\hat{p}$ = 0.2596

SE =

/pa/n V0.7404 x 0.2596/801 0.0155

Margin of Error, E = Z X SE = 1.645 X 0.0155 = 0.0255

(c)

Confidence Interval:

0.7404 $\pm$ 0.0255

= ( 0.7149 ,0.7659)

So,

Confidence Interval:

0.715 < p < 0.766

(d)

Three possible values:

0.72, 0.73, 0.74

(e)

The results doe not contradict the claim that 75% of peas are green.

Explanation:

0.75 is included in the Confidence Interval.