8. A researcher is interested in knowing whether the proportion of childless couples in acommunity deviates significantly from the statewide average of 0.12. A sample of 150couples is interviewed, and the mean proportion of childless couple in this sample is 0.17.Can you determine whether the researcher should accept the notion that the "true"proportion could be 0.12?9. A survey of two local communities is conducted to see whether there is difference in themean lengths of unemployment. Sample information, Community A: sample mean =12.4months, s=3, n=15; Community B: sample mean =14.4 months, s=4, n=15. Is there asignificant difference? Assuming equal variances, state the null and alternative hypotheses,and test the null hypothesis, using a=0.05. Find p=values and a 95% confidence interval forthe difference.10. Using the following hypothetical data:(a) Find the mean and standard deviation for each day of the week.(b) Use SPSS to carry out Levene's test to determine whether the assumption ofhomoscedasticity is satisfied.(c) Perform an analysis of variance to test the null hypothesis that precipitation does notvary by day of the week. Show the between and within sum of squares, the observed F-statistic, and the critical F-value.Precipitation at a rural town (Inches)SUNMONTUEWEDTHURFRISATWeek 1Week 2Week 35.553.371.723.190.781.075.572.451.441.661.642.632.322.802.202.343.403.683.482.502.75Week 44.312.021.834.354.072.662.23Week 52.663.952.311.852.631.113.65Week 63.002.612.454.064.96

Answered: 8. A researcher is interested in…

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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8. A researcher is interested in knowing whether the proportion of childless couples in a
community deviates significantly from the statewide average of 0.12. A sample of 150
couples is interviewed, and the mean proportion of childless couple in this sample is 0.17.
Can you determine whether the researcher should accept the notion that the "true"
proportion could be 0.12?
9. A survey of two local communities is conducted to see whether there is difference in the
mean lengths of unemployment. Sample information, Community A: sample mean =12.4
months, s=3, n=15; Community B: sample mean =14.4 months, s=4, n=15. Is there a
significant difference? Assuming equal variances, state the null and alternative hypotheses,
and test the null hypothesis, using a=0.05. Find p=values and a 95% confidence interval for
the difference.
10. Using the following hypothetical data:
(a) Find the mean and standard deviation for each day of the week.
(b) Use SPSS to carry out Levene's test to determine whether the assumption of
homoscedasticity is satisfied.
(c) Perform an analysis of variance to test the null hypothesis that precipitation does not
vary by day of the week. Show the between and within sum of squares, the observed F-
statistic, and the critical F-value.
Precipitation at a rural town (Inches)
SUN
MON
TUE
WED
THUR
FRI
SAT
Week 1
Week 2
Week 3
5.55
3.37
1.72
3.19
0.78
1.07
5.57
2.45
1.44
1.66
1.64
2.63
2.32
2.80
2.20
2.34
3.40
3.68
3.48
2.50
2.75
Week 4
4.31
2.02
1.83
4.35
4.07
2.66
2.23
Week 5
2.66
3.95
2.31
1.85
2.63
1.11
3.65
Week 6
3.00
2.61
2.45
4.06
4.96

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$Null Hypothesis (H_{0}) : p = 0.12, i . e the true proportion is 0.12 Alternative Hypothesis (H_{1}) : p \neq 0.12$

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