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Sladkaya [172]
3 years ago
7

ind the value of the test statistic z using z equals StartFraction ModifyingAbove p with caret minus p Over StartRoot StartFract

ion 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.
Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
6 0

Answer:

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

Step-by-step explanation:

Data given and notation

n=530 represent the random sample taken

X=139 represent the yellow pods in the random sample

\hat p=\frac{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 \neq 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{\frac{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{\frac{0.25(1-0.25)}{530}}}=0.638  

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