Respuesta :
The test static value is 1.44 and its associated p-value is 0.1335.
Given that the problem deals with the concept of test for single proportion. The parameter of the interest is the population proportion of graduates with GPA of 3.00 or below is less than 0.09.
Let the population proportion be p=0.09.
Let the number of graduates in a sample be n=260.
Let the number of students have a GPA of 3.00 or below be x=20.
Based on the known data, the null and alternative hypothesis are,
H₀:p≥0.09
H₁:p<0.09
The sample proportion of students have a GPA of 3.00 or below is,
[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\ &=\frac{20}{260}\\ &=0.07\end[/tex]
Under the null hypothesis, the test static value is,
[tex]\begin{aligned}z&=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\ &=\frac{0.07-0.09}{\sqrt{\frac{0.09(1-0.09)}{260}}}\\ &=\frac{-0.02}{0.018}\\ &=-1.11\end[/tex]
The p-value for the left-tailed test is
p-value=p(z<-1.11)
p-value=0.1335
Hence, the value of the test statistic and its associated p-value for the proportion of graduates with a GPA of 3.00 or below is less than 0.09. are 1.44 and 0.1335.
Learn more about null hypothesis from here brainly.com/question/9954556
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