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A recent study used umbilical cord blood to test for 25 hydroxyvitamin D, which is an indicator of vitamin D status of the baby. It was reported that 65% of babies tested were deficient in vitamin D in spite of the fact that the mothers consumed vitamin D supplements during pregnancy. A researcher in a northern region felt that this percentage was too high for this region because with the reduced hours of sunshine during winter months, pregnant women tended to use higher doses of supplements to compensate. A sample of 125 newborns was tested, and 72 were declared to be deficient in vitamin D. What would be the appropriate null and alternative hypotheses that the researcher should establish for a test of significance?

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ajeigbeibraheem

Answer:

Null hypothesis: p= 0.65

Alternative Hypothesis: p  < 0.65

Explanation:

Below are the null and alternative hypothesis,

Null hypothesis: p= 0.65

Alternative Hypothesis: p  < 0.65

Test  statistic for text of significance  

z = (pcap –p)/ [tex]\sqrt{ [p*(1-p)/n]}[/tex]

z = (0.576 – 0.65)/ [tex]\sqrt{[0.65×1-0.65)/125]}[/tex]

z = 1.73

P- value Approach

p-value = 0.0414

 

As P-value < 0.05,  we reject the null hypothesis

 There is sufficient evidence  to  conclude that the mother consumed vitamin D supplements during pregnancy. A researcher in a northern region felt that the percentage should be lower for this region because with reduced hours of sunshine during winter months, pregnant women tended to use of higher doses of supplements to compensate.

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