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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

Respuesta :

Answer:

[tex]z=\frac{256-266}{\frac{16}{\sqrt{20}}}=-2.795[/tex]    

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

[tex]p_v =P(z<-2.795)=0.0026[/tex]  

Step-by-step explanation:

Information provided

[tex]\bar X=256[/tex] represent the sample mean

[tex]\sigma=16[/tex] represent the population standard deviation

[tex]n=20[/tex] sample size  

[tex]\mu_o =266[/tex] represent the value that we want to test

z would represent the statistic

[tex]p_v[/tex] 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:[tex]\mu \geq 266[/tex]  

Alternative hypothesis:[tex]\mu < 266[/tex]  

The statistic is given by:

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

Replacing the info given we got:

[tex]z=\frac{256-266}{\frac{16}{\sqrt{20}}}=-2.795[/tex]    

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

[tex]p_v =P(z<-2.795)=0.0026[/tex]  

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