In: Statistics and Probability
A genetic experiment with peas resulted in one sample of offspring that consisted of 409 green peas and 159 yellow peas.a. Construct a 90% 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?
Given,
Number of green peas = 409
Number of yellow peas = 159
Total peas n = 409 + 159 = 568
Sample proportion of yellow peas = = 159 / 568 = 0.27993
Confidence interval for population proportion is given by,
Where, is z critical value at given confidence level
Confidence level = 90% = 0.9
Significance level = = 1 - 0.9 = 0.1
= = 1.645 , { Using Excel, = normsinv( 0.025 ) = 1.645 }
So, 90% confidence interval for proportion of yellow peas is,
CI = ( 0.24894 , 0.31092 )
90% confidence interval for proportion of yellow peas is ( 0.24894 , 0.31092 )
No, the confidence interval includes? 0.25, so the true percentage could be equal? 25%