1. A sample of size 9 is collected from a population which has a standard deviat
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Question
1. A sample of size 9 is collected from a population which has a standard deviation of 5. The sample mean is calculated as 20. What is the confidence interval under 90% confidence level?
2. In HW5 part c, with your Excel sheet output for the regression, by looking at the p-value, compared with the significance level of 0.05, do you think the true intercept is different from 0? Do you think the true slope is different from 0?
part c:
Given the sample collected bellow:
X: 3, 2, 5, 7, 3
Y: 9, 5, 12, 15, 8
Calculate manually the following:
c) use excel to report the 99% confidence intervals of the true intercept alpha and the true slope beta (your regression output in excel should confirm your manually calculated a and b estimates.)
Regression Statistics MultipleR R Square Adjusted R Square0.942176871 Standard Error Observation 0.978075996 0.956632653 0.921954446 ANOVA MS Significance F Regression Residual Total 56.25 2.55 58.8 56.2566.17647059 0.00388401 0.85 4 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% U r99.0% Intercept X Variable 1 2.3 1.0099504942.277339349 0.1071975480.914113218 5.514113218-3.5990292428.199029242 2.608517630.528736924 3.221263076 1.875 0.2304886118.134892168 0.00388401 1.14148237Explanation / Answer
= M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level=1.64
sM = standard error = (s2/n)= (92/5) = 4.02
= 20 ± 1.64*4.02
= 20 ± 6.62
90% CI [13.38, 26.62]
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