ANSWER NUMBER 8 28400 older were marrled opulation of Americans age 18 and (10%)
ID: 3322810 • Letter: A
Question
ANSWER NUMBER 8
28400 older were marrled opulation of Americans age 18 and (10%) According to the U.S. recent sample of 2400 American Census Bureau in 2014, 60% of Americans age 18 and 01 s age 18 and older showed that 58% of them are married. Construc older who are married (a) t a 95% confidence interval for the percentage o 5% significance level in favor of the alternative that the f Americans age 18 and older who are married is lower than 60%?? (b) Can you reject the null hypothesis at a percentage of current population o 8. 10%) A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that up to 16 ounces of ice cream. The food service manager is interested in comparing the average amount of ice cream dispensed by male students to the average amount dispensed by female students. A measurement device was placed on the ice cream machine to determine the amounts dispensed. Random ples of 100 male and 100 female students who got ice cream were selected. The sample averages were ounces for the male and female students, respectively. Assume that the population standard 7.5 and 6.5 deviations are 1.6 and 1.2 ounces, respectively. Let Ha and Ha be the population means of ice c amounts dispensed by all male and all female students at this college, respectively. (a) Construct a 95% confidence interval for (b) using a 5% significance level, can you conclude that the average amount of ice cream dispensed by all male college students is larger than the average amount dispensed by all female college students?Explanation / Answer
(a)
n1 = 100
n2 = 100
x1-bar = 7.5
x2-bar = 6.5
s1 = 1.6
s2 = 1.2
% = 95
Degrees of freedom = n1 + n2 - 2 = 100 + 100 -2 = 198
Pooled s = (((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/DOF) = (((100 - 1) * 1.6^2 + ( 100 - 1) * 1.2^2)/(100 + 100 -2)) = 1.414213562
SE = Pooled s * ((1/n1) + (1/n2)) = 1.4142135623731 * ((1/100) + (1/100)) = 0.2
t- score = 1.972017432
Width of the confidence interval = t * SE = 1.97201743225589 * 0.2 = 0.394403486
Lower Limit of the confidence interval = (x1-bar - x2-bar) - width = 1 - 0.394403486451179 = 0.605596514
Upper Limit of the confidence interval = (x1-bar - x2-bar) + width = 1 + 0.394403486451179 = 1.394403486
(b)
Since 0 lies outside the 95% confidence interval, we reject Ho and accept Ha. There is a significant difference in the volumes of ice creams dispensed.
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