9. A genetic experiment with peas resulted in one sample of offspring that consisted of 408 green peas and 160 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 not25%, do the results contradict expectations?
a. a. Construct a 95% confidence interval. Express the percentages in decimal form.
____<p<____
(Round to three decimal places as needed.)
Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?
No, the confidence 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%
Solution :
Given that,
a) n = 408 + 160 = 568
x = 160
Point estimate = sample proportion =
= x / n = 160 / 568 = 0.282
1 -
= 1 - 0.282 = 0.718
At 95% confidence level
= 1 - 95%
=1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.960
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 1.96 (((0.282
* 0.718) / 568)
= 0.037
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.282 - 0.037 < p < 0.282 + 0.037
(0.245 < p < 0.319)
b) Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%
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