Complete Question
The complete question is shown on the first uploaded image
Answer:
the null hypothesis is [tex]H_o : \mu = 122[/tex]
the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]
The test statistics is [tex]t = - 1.761[/tex]
The p-value is [tex]p = P(Z < t ) = 0.039119[/tex]
so
[tex]p \ge 0.01[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 122[/tex]
The sample size is n= 38
The sample mean is [tex]\= x = 116 \ feet[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
Generally the null hypothesis is [tex]H_o : \mu = 122[/tex]
the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }[/tex]
[tex]t = - 1.761[/tex]
The p-value is mathematically represented as
[tex]p = P(Z < t )[/tex]
From the z- table
[tex]p = P(Z < t ) = 0.039119[/tex]
So
[tex]p \ge 0.01[/tex]
