Answer:
There is no sufficient evidence to support the claim
Step-by-step explanation:
From the question we are told that
The level of significance is [tex]\alpha = 0.05[/tex]
The sample proportion is [tex]\r p = 0.08[/tex]
The sample size is [tex]n = 250[/tex]
Generally for normal sampling distribution can be used
[tex]n * p > 5[/tex]
So
[tex]n* p = 250 * 0.12 = 30[/tex]
Since
[tex]n * p > 5[/tex] then normal sampling distribution can be used
The null hypothesis is [tex]H_o : p = 0.12[/tex]
The alternative hypothesis is [tex]H_a : p > 0.12[/tex]
The test statistic is evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p)}{n} } }[/tex]
substituting values
[tex]t = \frac{0.08 - 0.12 }{ \sqrt{ \frac{0.12 (1- 0.12)}{250 } } }[/tex]
[tex]t = -1.946[/tex]
The p-value is obtained from the z table and the value is
[tex]p-value = P(t > -1.9462) =0.97512[/tex]
Since the [tex]p-value > \alpha[/tex]
Then we fail to reject the null hypothesis
Hence it means there is no sufficient evidence to support the claim
