Answer :
Answer:
There is not enough evidence that their efforts have paid of. The stations are not showing less leakage.
Step-by-step explanation:
The population proportion of service station that has gas storage tanks that leak to some extent is p = 0.40.
To test whether this proportion has decreased the hypothesis can be defined as:
H₀: The proportion of service stations whose tanks leak has not decreased, i.e. p ≥ 0.40.
Hₐ: The proportion of service stations whose tanks leak has decreased, i.e. p < 0.40.
Given:
n = 27
X = number of service stations whose tanks leak = 7
The sample proportion of service stations whose tanks leak is:
[tex]\hat p =\frac{X}{n} =\frac{7}{27} =0.2593[/tex]
Assume that the significance level of the test is α = 5%.
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{ \frac{p(1-p)}{n} }}=\frac{0.2593-0.40}{\sqrt{\frac{0.40(1-0.40}{27}}} =-1.49[/tex]
The value of test statistic is -1.49.
Decision rule:
If the p value is less than the significance level the null hypothesis will be rejected and vice-versa.
The p-value of the test statistic is:
[tex]P(Z<-1.49)=1-P(Z<1.49)=1-0.9319=0.0681[/tex]
The p-value = 0.0681 > α = 0.05.
Thus, the null hypothesis is not rejected at 5% level of significance.
Conclusion:
As the null hypothesis was not rejected at 5% level of significance, it can be concluded that the proportion of service stations whose tanks leak has not decreased.