g Total blood volume (in ml) per body weight (in kg) is important inmedical research. For healthy adults, the red blood cell volumemean is about μ=28 mg/kg. Red blood cell volume that is toolow or too high can indicate a medical problem. Suppose Roger has seven blood tests, and the mean is 32.7 m//kg. Suppose that red blood cell volume follows normal distribution with standard deviation 4.75 ml/kg. With 5% level of significance, test that the mean blood cell volume is different from 28 ml/kg?

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 28 at 5% of significance.

Step-by-step explanation:

Information given

[tex]\bar X=32.7[/tex] represent the sample mean for the blood cell

[tex]\sigma=4.75[/tex] represent the population standard deviation

[tex]n=7[/tex] sample size

[tex]\mu_o =28[/tex] represent the value to check

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to verify if the mean blood cell volume is different from 28 ml/kg the system of hypothesis would be:

Null hypothesis:[tex]\mu = 28[/tex]

Alternative hypothesis:[tex]\mu \neq 28[/tex]

Since we know the population deviation we can use the following statistic:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)

Replacing the info given we got:

[tex]z=\frac{32.7-28}{\frac{4.75}{\sqrt{7}}}=2.618[/tex]

Now we can calculate the p value with this probability:

[tex]p_v =2*P(Z>2.618)=0.0088[/tex]

Since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significanctly different from 28 at 5% of significance.