Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 475 green peas and 193 yellow peas. Find the 94% confidence interval to estimate the percentage of yellow peas. It was expected that 25% of the offspring peas would be yellow, do the results contradict the expectations? Round to the hundredths place of a percent-do not enter the % symbol.

Answer 1

Given:

Number of green peas = 475

Number of yellow peas = 193

Let's find the 94% confidence interval to estimate the percentage of yellow peas.

Where:

Total number of peas = 475 + 193 = 668

For the sample proportion, we have:

$\begin{gathered} p^{\prime}=\frac{194}{668} \\ \\ p^{\prime}=0.2889 \end{gathered}$

For a 94% confidence interval, the significance level will be:

1 - 0.94 = 0.06

For the critical value, using the z-table, we have:

$z_{\frac{\alpha}{2}}=z_{\frac{0.06}{2}}=z_{0.03}=1.881$

Now, to find the 94% confidence interval, apply the formula::

Where:

To find the margin of error E, we have:

$E=z_{\frac{\alpha}{a}}*\sqrt{\frac{p^{\prime}(1-p^{\prime})}{n}}=1.881*\sqrt{\frac{0.2889(1-0.2889)}{668}}=0.032987$

Thus, we have:

[tex]\begin{gathered} p^{\prime}-E

Hence the confidence interval will be:

Lower limit = 0.2559 ==> 25.59%

Upper limit = 0.3219 ==> 32.19 %

The confidence interval does not contain 0.25, hence we can say that the true results contradicts the expectations.

ANSWER:

The confidence interval does not contain the expectation of 25%, hence, the true results contradicts the expectation.