ab9.2113.513.513.714.214.515.315.8117.117.517.717.817.918.018.318.818.819.019.9120.220.5120.721.6122.122.7122.723.624.9126.9127.9Screenshot The data below is from a random sample of married women drawn from the population of anurban area in a less-developed country. This data has two variables; 'a' is the age at which eachwoman was married for the first time, 'b’ is whether or not at least one of their parents had asecondary or higher education (0=no, 1=yes).1) Estimate the sample mean, variance, standard deviation, and standard error for age at firstmarriage for the entire population. Calculate the 95% confidence interval around thisestimate and interpret.2) Repeat the analysis from 1) above for each parental education group (*b’) separately. Dothe confidence intervals overlap?3) We hypothesize that children of more educated parents will marry later than children ofless well educated parents. Perform a two-sample t-test of this hypothesis, using thefolowing formula (the standard error for a two sample t-test combines the standard errorsof each group) and interpret your result. Group l' will be those whose parents had moreeducation, group '2' will be those whose parents had less.X – x2-+n1n2

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Description: ab9.2113.513.513.714.214.515.315.8117.117.517.717.817.918.018.318.818.819.019.9120.220.5120.721.6122.122.7122.723.624.9126.9127.9Screenshot The data below is from a random sample of married women drawn from the population of anurban area in a less-d

Answered: The data below is from a random sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The data below is from a random sample of married women drawn from the population of an
urban area in a less-developed country. This data has two variables; 'a' is the age at which each
woman was married for the first time, 'b’ is whether or not at least one of their parents had a
secondary or higher education (0=no, 1=yes).
1) Estimate the sample mean, variance, standard deviation, and standard error for age at first
marriage for the entire population. Calculate the 95% confidence interval around this
estimate and interpret.
2) Repeat the analysis from 1) above for each parental education group (*b’) separately. Do
the confidence intervals overlap?
3) We hypothesize that children of more educated parents will marry later than children of
less well educated parents. Perform a two-sample t-test of this hypothesis, using the
folowing formula (the standard error for a two sample t-test combines the standard errors
of each group) and interpret your result. Group l' will be those whose parents had more
education, group '2' will be those whose parents had less.
X – x2
-
+
n1
n2

Expert Solution

Step 1

We have,

n = 30

n₁= n₂ = 15

We compute the mean, variance, standard deviation and standard error for age at first marriage for the entire population.

We first compute the mean variance and standard deviation using excel formula as below:

Thus, we have,

Mean = 18.81

Variance = 17.6299

Standard deviation = 4.198797.

Standard error = Standard deviation/√n = 4.198797/√30 = 0.766592.

The 95% confidence interval for population mean for age at first marriage for the entire population is computed as,

$C I = \bar{x} \pm t_{α / 2, n - 1} \frac{s}{\sqrt{n}} = 18.8 \pm 2.0452 \frac{4.198797}{\sqrt{30}} (f r o m t - t a b l e) = 18.8 \pm 1.567857$

Thus, the 95% confidence interval for population mean for age at first marriage for the entire population is (17.23214, 20.36786)

The 95% confidence interval for population mean indicates that there is 95% chance that the true population will be contained in this interval.

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