Respuesta :
a) 90% confidence interval is 0.275 + or - 0.031 of the percentage of yellow peas.
b) Yes, based on the confidence interval, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow.
a) Yellow pea sample percentage = 159 ÷ (420 + 159) = 0.275
standard deviation = √(0.275 × (1 = 0.275) ÷ (420 + 159)) = 0.019
alpha(a) = 1 - (90 ÷ 100) = 0.10
critical probability(p*) = 1 - (a ÷ 2) = 0.95
Assume that the population is evenly distributed and that because the sample size is more than 30, a normality assumption is utilized to calculate the 90% sampling error.
The crucial value for the z-score linked with p* is 1.645. (CV).
Margin of error = CV × SE = 1.645 × 0.019 = 0.031
The 90% confidence interval is 0.275 + or - 0.031, (0.244, 0.306)
b) The 90% confidence level indicates that we should anticipate the population proportion of yellow peas to be included in 90% of the confidence level estimations.
H0: X = 0.25
H1: X not = 0.25
H0 denotes the null hypothesis, while H1 denotes a two-tailed test.
z = (0.275 - 0.25) ÷ 0.019 = 1.316
Because this is a two-tailed check, reject H0 if 1.316 > 1.96 or if 1.316 < -1.96, but we do not reject H0 if 1.316 < 1.96.
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The question is -
A genetic experiment with peas resulted in one sample of offspring that consisted of 420 green peas and 159 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
