Question

Find the value of the test statistic z using z equals StartFraction ModifyingAbove p with caret minus p Over StartRoot StartFraction pq Over n EndFraction EndRoot EndFraction . The claim is that the proportion of peas with yellow pods is equal to 0.25​ (or 25%). The sample statistics from one experiment include 590 peas with 180 of them having yellow pods. zequals nothing ​(Round to two decimal places as​ needed.)

Answer 1

3.09

Explanation:

The sample proportion can be calculated as phat=x/n

phat=180/590=0.305

The z statistic for proportion can be calculated as

`Z=\frac{phat-p}{\sqrt{(pq)/(n) } }`

Where p=population proportion=0.25

q=1-p=1-0.25=0.75

n=590

phat=sample proportion=0.305

So, the required z-statistic is

`Z=\frac{0.305-0.25}{\sqrt{(0.25(0.75))/(590) } }`

`Z=\frac{0.055}{\sqrt{(0.1875)/(590) } }`

`Z=(0.055)/(√(0.0003178 ) )`

z=3.085

As the rounding of answer to two decimal places is needed, so, the z statistic=3.09.