Answer:
The p- value is [tex]p-value = 0.2033[/tex]
Its interpretation is
As [tex]p-value > \alpha[/tex]
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to support the company claims at a level of sign9ificance of 0.05
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 30 \ inches[/tex]
The standard deviation is [tex]\sigma = 1.2 \ inches[/tex]
The sample size is n = 100
The sample mean is [tex]\= x = 30.1[/tex]
Let assume the level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu \le 30[/tex]
The alternative is [tex]H_a : \mu > 30[/tex]
Generally the test test is mathematically represented as
[tex]z = \frac{\= x- \mu }{\frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{30.1- 30 }{\frac{1.2}{\sqrt{100} } }[/tex]
=> [tex]z = 0.83[/tex]
Generally from the z-table the probability of (Z > 0.83 ) is
[tex]p-value = 0.2033[/tex]
From the value obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to support the company claims at a level of sign9ificance of 0.05
