Question

How to find the Test Statistic??? (TI-84+)
My question says: A genetic experiment involving peas yielded one sample of offspring consisting of 444 green peas and 179 yellow peas. Use a .01 significance level to the the claim that under the same circumstances, 26% of offspring will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P-vale, conclusions about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

I know the null and alternative hypothesis is: p=.26 and p=/ .26

Then it asks for the test statistic z = ?
On my calculator I put Stat --> Tests --> 1-PropZTest
Po:.26
x: 162 (.26*623)
n:623

When I calculate my answer is: z = -10.50
but my computer says it's wrong. When I look in the "help" option, it doesn't show the calculator steps.

Answer 1

The test statistic would be
\[Z=\frac{\hat{p}-p_0}{\sqrt{\dfrac{p_0(1-p_0)}{n}}}\]
where \(\hat{p}\) is the estimated proportion of yellow peas, \(p_0\) is the proportion assumed under the null hypothesis, and \(n\) is the sample size. Here, \(p_0=0.26\), while \(\hat{p}=\dfrac{179}{179+444}\approx0.29\), so you should have
\[Z=\frac{0.29-0.26}{\sqrt{\dfrac{0.26(1-0.26)}{623}}}\approx 1.707\]