Quantitative Methods: Confidence Interval and Estimators

QUANTITATIVE METHODS
Student Name
[Pick the date]

Part A
Question 1
(a) Calculation of 95% confidence interval
Set of data observation = n= 12
Average of data (x bar) = (745+752+754+745+748+753+746+742+745+748+741+746)/12
=747.083
Standard deviation
For 95% confidence interval, z value = 1.960
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(b) Null and alternative hypotheses
Dof =12−1=11
Hypothesis testing = Two tailed test
The respective p value (for input, test statistics, dof and two tailed test) = 0.0321
Let the alpha (significance level) = 5%
The p value << alpha
Reject null hypothesis and can be concluded that “standard bottles of wine does not contain an
average of exactly 750 ml.”
(c) A key observation is that the confidence interval computed in part (a) does not contain the
value 750 which implies that it is not a possible value and hence there is significant
difference from 750 ml. This clearly is same as the outcome in part (b).
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