19.5 20.3 19.6 20.2 17.8 17.9 19.1 18.8 17.6 16.8 Tthe answer isbelow, I need he

Question

19.5    20.3   19.6    20.2   17.8    17.9   19.1    18.8    17.6     16.8

Tthe answer isbelow, I need help with the steps, thank you

H0 : = 20.16,H1 : < 20.16. Test stat t = 3.732CV z = 2.82, P-value < 0.005 tech 0.0023. RejectH0. Recent winner appear to besignificantly different than those who were ourgreat-grandmothers.

H0 : = 20.16,H1 : < 20.16. Test stat t = 3.732CV z = 2.82, P-value < 0.005 tech 0.0023. RejectH0. Recent winner appear to besignificantly different than those who were ourgreat-grandmothers.

Explanation / Answer

we have to test the claim that recent Miss America winners arefrom a population with a mean BMI less than 20.16 for the above objetive, we set up the null hypothesis, H0:  recent Miss America winnersare from a population with a mean BMI 20.16                       = 20.16 against H1:  recent Miss America winners are froma population with a mean BMI less than 20.16                      <20.16 (left tailed test) to test the above hypothesis, the BMIs of recent MissAmerica winners were taken, for which the mean is obtained as           sample mean, X bar = 18.76 and sample standard deviation, S = 1.186217 then the test statistic will be t = (X bar - ) / (S /n) = (18.76 - 20.16 ) /(1.186217/10) = -3.73219 the table value at 9df and at 0.05los is -1.833 since the calclulated value is less than the table value(lefttailed test) , we REJECT the null hypothesis hence, we may conclude that recent Miss America winners arefrom a population with a mean BMI less than 20.16

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