Q 8.150. - Elementary Statistics

Question

Christmas Spending. In a national poll of $1039$ U.S. adults, conducted November$7-10, 2013$, Gallup asked "Roughly how much money do you think you personally will spend on Christmas gifts this year?". The data provided on the Weiss Stats site are based on the results of the poll.

a. Determine a $95\%$ upper confidence bound for the mean amount spent on Christmas gifts in $2013$ (Note: The sample mean and sample standard deviation of the data are $\backslash (704.00$ and $\backslash )477.98$, respectively.)

b. Interpret your result in part (a).

c. In $2012$ , the mean amount spent on Christmas gifts was $\$770$. Comment on this information in view of your answer to part (b).

Step-by-Step Solution

Answer

Part (a) $728.413$

Part (b) The mean amount spent on Christmas gifts in $2013$ is lesser than the $728.413$

Part (c) The consumers spent more money in $2012$ when compared to the $2013$

Part (a) Step 1: Given information

In a national poll of $1039$ individuals conducted on November $7-10, 2013$ The information on the Weiss Stats website is based on the poll results.

Part (a) Step 2: Concept

The formula used: Upper confidence bound $\overline{x}+t_{\alpha }·\frac{s}{\sqrt{n}}$

Part (a) Step 3: Explanation

Using MINITAB, calculate the $95\%$ upper confidence bound for the mean amount spent on Christmas gifts in $2013$

Procedure for MINITAB:

Step 1: Select Stat > Basic Statistics > $1-$Sample $t$ from the drop-down menu.

Step 2: In Summarized Data, enter $1,039$ as the sample size and $704$ as the mean.

Step 3: In the Standard deviation box, type $477.98$ for $s$

Step 4: Select Options and set the Confidence Level to $95$

Step 5: Choose the less expensive option.

Step 6: In all dialogue boxes, click OK.

OUTPUT FROM MINITAB: 

One-Sample T

N	Mean	StDev	SE Mean	95% Upper Bound
1039	704.000	477.980	14.829	728.413

The $95\%$ upper confidence bound for the mean amount spent on Christmas gifts in $2013$ is $728.41$, according to MINITAB output.

Part (b) Step 1: Explanation

There is a $95\%$ chance that the average amount spent on Christmas gifts in 2013 will be less than $728.413$

Part (c) Step 1: Explanation

Part (b) shows that there is $95\%$ confidence that the average amount spent on Christmas presents in $2013$ is less than the average amount spent on Christmas gifts in $2012$, implying that customers spent more money in $2012$ than in $2013$