Answer:
The correct option is a
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 30\ seconds[/tex]
The standard deviation is [tex]\sigma = 3 \ seconds[/tex]
The sample size is n = 9
The null hypothesis is [tex]H_o: \mu = 30[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 30[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The sample mean is [tex]\= x = 31.2[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{ 31.2 - 30}{ \frac{3}{\sqrt{9} } }[/tex]
=> [tex]z = 1.2[/tex]
From the z table the area under the normal curve to the right corresponding to 1.2 is
[tex]P(Z > 1.2) = 0.11507[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(Z > 1.2)[/tex]
=> [tex]p-value = 2 *0.11507[/tex]
=> [tex]p-value = 0.230[/tex]
From the value obtained w can see that
[tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is there is not enough evidence to support the claim
