Complete Question
A random sample of 114 observations produced a sample mean of 30. Find the critical and observed values of z for the following test of hypothesis using α=0.01. The population standard deviation is known to be 5 and the population distribution is normal.
[tex]H_o: \mu =28[/tex] versus H1: μ>28.
Round your answers to two decimal places.
[tex]z_{critical} =[/tex]
Answer:
[tex]z_{critical} = 2.33[/tex]
The observed value is [tex] z = 4.27 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 114
The sample mean is [tex]\= x = 30[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
The population standard deviation is [tex]\sigma = 5[/tex]
The null hypothesis is [tex]H_o: \mu =28[/tex]
The alternative hypothesis is H1: μ>28.
Generally the test statistics (observed value ) is mathematically represented as
[tex] z = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } } [/tex]
=> [tex] z = \frac{ 30- 28 }{ \frac{5}{\sqrt{114} } } [/tex]
=> [tex] z = 4.27 [/tex]
From the normal distribution table the critical value of [tex]\alpha = 0.01[/tex] is
[tex]z_{critical} = 2.33[/tex]
