Three hundred (300) young males and 350 young females aged 15 to 24 were randomly selected for a STEPS survey in Trinidad and Tobago in 2018. STEPS surveys are regularly carried out in Trinidad and Tobago to identify the major risk factors that determine the major diseases burden among teenagers. The mean height among the male sample is 175 cm, while the mean height among the sample of female is 161 cm. The corresponding sample standard deviations for the two groups of young persons are 8.0 cm and 8.2 cm, respectively. (1.)State the estimator you would use to estimate the difference in the mean height between young males and females. Define the probability distribution of this estimator. (2.)Calculate the 86% confidence interval for the difference in the mean height between young males and young females in the age group 15-24 in Trinidad and Tobago. Write your answer to 3 decimal places. (3.)Test the hypothesis that the mean heights for young males and females in the age group 15-24 are equal. Test at the 5% level of significance.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Three hundred (300) young males and 350 young females aged 15 to 24 were randomly selected for a STEPS survey in Trinidad and Tobago in 2018. STEPS surveys are regularly carried out in Trinidad and Tobago to identify the major risk factors that determine the major diseases burden among teenagers. The
(1.)State the estimator you would use to estimate the difference in the mean height between young males and females. Define the probability distribution of this estimator.
(2.)Calculate the 86% confidence interval for the difference in the mean height between young males and young females in the age group 15-24 in Trinidad and Tobago. Write your answer to 3 decimal places.
(3.)Test the hypothesis that the mean heights for young males and females in the age group 15-24 are equal. Test at the 5% level of significance.
ANWER 1,2,3 . SHOW ALL WORKING
Given :
Male :
mean = 175
sample size = n = 300
standard deviation = 8
Female :
mean = 161
standard deviation = 8.2
sample size = n = 350
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