Answer :
Answer:
Decision rule
Reject null hypothesis
Conclusion
There is significance evidence that the true mean is different from 0.86
Step-by-step explanation:
From the question we are told that
The population mean [tex]\mu = 0.86[/tex]
The sample is mean is [tex]\= x = 0.8708[/tex]
The standard deviation is [tex]\sigma = 0.0068[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The sample size n = 3
The null hypothesis is [tex]\mu = 0.86[/tex]
The alternative hypothesis is [tex]\mu \ne 0.86[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{ 0.8708 - 0.86 }{ \frac{0.0068}{\sqrt{3} } }[/tex]
=> [tex]z = 2.751 [/tex]
Generally p- value is mathematically represented as
[tex]p-value = 2 P(z >2.751 )[/tex]
From the z-table
[tex]P(z >2.751 ) = 0.0029707[/tex]
So
[tex]p-value = 2 * 0.0029707[/tex]
=> [tex]p-value = 0.00594 [/tex]
From the obtained question we see that [tex]p-value < \alpha[/tex]
Hence we reject the null hypothesis