Question

The human average gestation time is 266 days from conception. A researcher suspects that proper nutrition plays an important role and that poor women with inadequate food intake should have shorter gestation times even when given vitamin supplements. A random sample of 20 poor women given vitamin supplements throughout the pregnancy has mean gestation time from conception x = 256 days. Human gestation times are approximately Normal with standard deviation ? = 16 days. The P -value for the researcher

Answer 1

Answer:

$z=\frac{256-266}{\frac{16}{\sqrt{20}}}=-2.795$    

The p value for this case can be calculated with this probability:

$p_v =P(z<-2.795)=0.0026$  

Step-by-step explanation:

Information provided

$\bar X=256$ represent the sample mean

$\sigma=16$ represent the population standard deviation

$n=20$ sample size  

$\mu_o =266$ represent the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Hypothesis to verify

We need to conduct a hypothesis in order to see if inadequate food intake should have shorter gestation times, the system of hypothesis would be:  

Null hypothesis:$\mu \geq 266$  

Alternative hypothesis:$\mu < 266$  

The statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$  (1)  

Replacing the info given we got:

$z=\frac{256-266}{\frac{16}{\sqrt{20}}}=-2.795$    

The p value for this case can be calculated with this probability:

$p_v =P(z<-2.795)=0.0026$