In the first problem, we calculated margin error =0.011, the 2nd problem we got population mean = 20.784 0r 19.216. the last problem true average age = 25.58 or 24.42
the margin of error indicates the differences between true result and estimated result.
The population means refers the average value of whole population where sample means indicate the average value of randomly selected samples only.
Given, size of population, n= 1936
random size of population, p = 121
probability 0.95 that means 95% confidence interval.
now margin error of sample mean is calculated by the following formula
Margin of error, ME= Z*×[√{p^(1-p^)/n}]
where, p^ is proportion of population and p^= p/n
z* is the critical value of 95% confidence interval
p^ =p/n= 121/1936 =0.0625
z*= 1.96
hence, ME= 0.011
In the next problem, size of random sample, n= 144
sample mean, x⁻ = 20
population standard deviation, б = 4.8
confidence interval = 95.44% is equal to 95%
critical value z* =1.96
we need to estimate the population mean,μ by the following formula
μ = x⁻ ± z*(σ/√n)
=20±1.96 (4.8/√144)
hence population mean is 20.784 or 19.216
in the last samples, true average ages can be calculated by the formula
true average age = average age ±z*(σ/√n)
given, standard deviation σ = 2
critical value for 98% confidence interval =2.33
size of sample, n= 64
average age =25
hence true average age = 25.58 or 24.42
hence, margin error is 0.011, population mean = 20. 784 or 19.216 and true average age = 25.58 or 24.42
to learn more about population means and sample means along with marginal error visit the link:
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