Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

question 190

Essay

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-Ten different families are tested for the number of gallons of water a day they use before and after viewing a
conservation video. At the 0.05 significance level, test the claim that the mean is the same before and after the
viewing. $$\begin{array} { l l l l l l l l l l l } \text { Before } & 33 & 33 & 38 & 33 & 35 & 35 & 40 & 40 & 40 & 31 \\\hline \text { After } & 34 & 28 & 25 & 28 & 35 & 33 & 31 & 28 & 35 & 33\end{array}$$

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Definitions:

Outstanding Checks

Checks that have been written and recorded in the accounting books but have not yet been cashed or cleared by the bank.

Non-Sufficient Funds

A situation where a bank account does not have enough money to cover a transaction, resulting in a failed payment.

Outstanding Checks

Checks that have been issued by a company but have not yet been cashed or cleared by the bank upon which they are drawn.

Bank Statement

A monthly report from a bank that shows deposits recorded, checks cleared, other debits and credits, and a running bank balance. This same information is available on a daily basis from the bank’s online banking site.