In: Statistics and Probability
A genetic experiment with peas resulted in one sample of offspring that consisted of
426426
green peas and
152152
yellow peas.
a. Construct a
9090%
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?
a. Construct a
9090%
confidence interval. Express the percentages in decimal form.
nothingless than<pless than<
nothing
(Round to three decimal places as needed.)
b. 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%
(a)
The genetic experiment was done with 426 green peas and 152 yellow peas.
So, the total number of the sample is:
n=426+152
=578
So, the point estimate of the proportion of yellow peas is:
p=152/578
=0.263
The critical value at 10% level of significance in Excel, is calculated as:
So, the confidence interval is calculated as:
Part a
The estimated percentage of yellow peas lies between .
Explanation | Common mistakes | Hint for next step
The confidence interval for the proportion of the yellow peas indicates that there is a 95% chance that the estimated percentage lies within the interval or 24.3% and 31.6%.
Step 2 of 2
(b)
The expectation is that 25% offspring peas would be yellow. But the percentage falls within the range of the confidence interval which is calculated for the proportion of yellow peas in the sample. It is provided that the percentage of offspring yellow peas is not 25%.
Part b
The provided results do not contradict the expectation.
Explanation
The provided information that the percentage of the offspring yellow peas is 25% does not contradict the calculated result, because the expected value lies within the confidence interval.