Question

ind 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 EndFractionz= p−p pq n. 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 530530 peas with 139139 of them having yellow pods.

Answer 1

`z=\frac{0.262 -0.25}{\sqrt{(0.25(1-0.25))/(530)}}=0.638`

Explanation:

Data given and notation

n=530 represent the random sample taken

X=139 represent the yellow pods in the random sample

`\hat p=(139)/(530)=0.262` estimated proportion of yellow pods

`p_o=0.25` is the value that we want to test

`\alpha` represent the significance level

z would represent the statistic (variable of interest)

`p_v` represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.25 or 25%:

Null hypothesis:
`p=0.25`

Alternative hypothesis:
`p \\eq 0.25`

When we conduct a proportion test we need to use the z statistic, and the is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

The One-Sample Proportion Test is used to assess whether a population proportion
`\hat p` is significantly different from a hypothesized value
`p_o`.

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

`z=\frac{0.262 -0.25}{\sqrt{(0.25(1-0.25))/(530)}}=0.638`