Answer :
Answer:
(0.23, 0.30)
Step-by-step explanation:
Number of green peas = 428
Number of yellow peas = 155
Total number of peas = n = 583
Since we have to establish the confidence interval for yellow peas, the sample proportion of yellow peas would be considered as success i.e. p = [tex]\frac{155}{583}[/tex]
q = 1 - p = [tex]\frac{428}{583}[/tex]
Confidence Level = 95%
Z value associated with this confidence level = z = 1.96
Confidence interval for the population proportion is calculated as:
[tex](p-z\sqrt{\frac{pq}{n}} ,p+z\sqrt{\frac{pq}{n}})[/tex]
Using the values, we get:
[tex](\frac{155}{583}-1.96\sqrt{\frac{\frac{155}{583} \times\frac{428}{583}}{583} },\frac{155}{583}+1.96\sqrt{\frac{\frac{155}{583} \times\frac{428}{583}}{583} })\\\\ =(0.23,0.30)[/tex]
Conclusion:
We are 95% confident that true value of population proportion of yellow peas lie between 0.23 and 0.30