Question

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%

 

Answer 1

(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.