Phenotypic variation exists in natural populations. There are many causes of variation. Natural selection determines which phenotypes are advantageous. （b）There is variation in the quantity of vitamin D stored in the body． Vitamin D has an important role in keeping bones healthy．The main storage form of vitamin D in the body is serum 25－hydroxyvitamin D（serum 25－OHD）． A study was carried out on 262 healthy women to investigate if the concentration of serum $$\(25-\mathrm{OHD}\)$$ varied between summer and winter．The women had taken no vitamin D supplements．The age range of the women in the sample was 40 to 72 years old． Table 5.2 shows the results of the study． Table 5.2 Additional analysis showed that there was no significant correlation between age and serum 25－OHD concentration． （i）Explain what is meant by standard deviation． ....................................................................................................................................... . ................................................................................................................................. ［1］ （ii）The $$\(t\)$$－test was used to compare the mean concentration of serum $$\(25-\mathrm{OHD}\)$$ when sampled during the summer with the mean concentration of serum $$\(25-\mathrm{OHD}\)$$ when sampled during the winter，as shown in Table 5．2． Calculate the value of $$\(t\)$$ using the formula provided． key to symbols： $$\(\bar{x}=\)$$ mean $$\(s=\)$$ sample standard deviation $$\(n=\)$$ sample size（number of observations） Give your answer to four significant figures． There is space for your working． State the conclusion that can be made about the results of the study shown in Table 5.2 and explain how the result of your calculation in (b)(ii) can be used to support this conclusion. ....................................................................................................................................... . ....................................................................................................................................... . ....................................................................................................................................... . ....................................................................................................................................... . ....................................................................................................................................... . ....................................................................................................................................... . ....................................................................................................................................... . ....................................................................................................................................... . ................................................................................................................................. (iv) Suggest the likely causes of variation in quantity of vitamin $$\(D\)$$ stored in the body in this sample of women. ....................................................................................................................................... . ....................................................................................................................................... . .................................................................................................................................

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