Answer:
There is enough evidence to conclude that the doctors claim is true
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 5kg[/tex]
The sample size is n = 50
The sample mean is [tex]\= x = 6.5 \ kg[/tex]
The standard deviation is [tex]\sigma = 2.2 \ kg[/tex]
The null hypothesis is [tex]H_o : \mu = 5kg[/tex]
The alternative hypothesis is [tex]H_a : \mu > 5kg[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 6.5 - 5 }{\frac{2.2}{\sqrt{50} } }[/tex]
=> [tex]t = 4.82[/tex]
The p-value is obtained from the z- table the value is
[tex]p- value = P(Z > 4.82)[/tex]
[tex]p- value = 0.00[/tex]
Seeing that [tex]p-value < \alpha[/tex] we reject the null hypothesis
Hence there is enough evidence to conclude that the doctors claim is true
