Sugar-Sweetened Beverages In 2017, the journal Obesity reported on trends in sugar-sweetened beverage (SSB) consumption. A random sample of youths aged 12 to 19 years old were asked to monitor all food and beverages consumed in a 24-hour period. The study was done in 2003 and repeated in 2014. The numbers who consumed a sugary beverage such as soda or fruit juice in a day are shown in the table. (Bleich et al., “Trends in Beverage Consumption among Children and Adults, 2003-2014,” Obesity, vol. 26 [2018]: 432-441. doi:10.1002/oby.22056) a. Calculate and compare the percentages of youths in this age group who consumed an SSB during the recording period. b. Check that the conditions for using a two-population confidence interval hold. c. Find the 95 % confidence interval for the difference in the proportion of youth consuming an SSB in 2003 and 2014. Based on your confidence interval, do you think there has been a change in sugar-sweetened beverage consumption among this age group? Explain.
Sugar-Sweetened Beverages In 2017, the journal Obesity reported on trends in sugar-sweetened beverage (SSB) consumption. A random sample of youths aged 12 to 19 years old were asked to monitor all food and beverages consumed in a 24-hour period. The study was done in 2003 and repeated in 2014. The numbers who consumed a sugary beverage such as soda or fruit juice in a day are shown in the table. (Bleich et al., “Trends in Beverage Consumption among Children and Adults, 2003-2014,” Obesity, vol. 26 [2018]: 432-441. doi:10.1002/oby.22056) a. Calculate and compare the percentages of youths in this age group who consumed an SSB during the recording period. b. Check that the conditions for using a two-population confidence interval hold. c. Find the 95 % confidence interval for the difference in the proportion of youth consuming an SSB in 2003 and 2014. Based on your confidence interval, do you think there has been a change in sugar-sweetened beverage consumption among this age group? Explain.
Solution Summary: The author compares the required percentages of youth who consumed SSB in 2003 and 2014.
Sugar-Sweetened Beverages In 2017, the journal Obesity reported on trends in sugar-sweetened beverage (SSB) consumption. A random sample of youths aged 12 to 19 years old were asked to monitor all food and beverages consumed in a 24-hour period. The study was done in 2003 and repeated in 2014. The numbers who consumed a sugary beverage such as soda or fruit juice in a day are shown in the table. (Bleich et al., “Trends in Beverage Consumption among Children and Adults, 2003-2014,” Obesity, vol. 26 [2018]: 432-441. doi:10.1002/oby.22056)
a. Calculate and compare the percentages of youths in this age group who consumed an SSB during the recording period.
b. Check that the conditions for using a two-population confidence interval hold.
c. Find the
95
%
confidence interval for the difference in the proportion of youth consuming an SSB in 2003 and 2014. Based on your confidence interval, do you think there has been a change in sugar-sweetened beverage consumption among this age group? Explain.
6. Show that
1{AU B} = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B};
I{AB} = min{I{A}, I{B}} = I{A} I{B};
I{A A B} = I{A} + I{B}-21{A} I {B} = (I{A} - I{B})².
Theorem 3.5 Suppose that P and Q are probability measures defined on the same
probability space (2, F), and that F is generated by a л-system A. If P(A) = Q(A)
for all A = A, then P = Q, i.e., P(A) = Q(A) for all A = F.
6. Show that, for any random variable, X, and a > 0,
Lo P(x
-00
P(x < x
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