Question #a2ec7

1 Answer
Solace M.
Sep 28, 2017

Sample Mean =35.5
Sample Standard Deviation ≈8.155
Given a 5% level of significance, these results have statistical significance.

Explanation:

To find the mean , we add all the values together, then divide them by how many numbers there were, so:
37+43+30+27+26+39+35+38+45+46+42+21+51+28+40+2016
=56816

=35.5, therefore the average age of the customers from this sample is 35.5 years old.

With a 5% level of significance, any luck or chance based events should affect the score only within
30⋅0.05=1.5 points. Since the average from this sample is higher then the level of significance, we can say that the score has statistical significance , and isn't merely due to a sampling error, thus rejecting the null hypothesis .

To find the standard deviation, we take the square root of the average squared distances from the mean. It looks like this:
(37−35.5)2
=(1.5)2
=2.25. We do this for the rest of the values to get:

(43−35.5)2=56.25and(30−35.5)2=30.25,
(27−35.5)2=72.25and(26−35.5)2=90.25,
(39−35.5)2=12.25and(35−35.5)2=0.25,
(38−35.5)2=6.25,and(45−35.5)2=90.25,
(46−35.5)2=110.25and(42−35.5)2=42.25,
(21−35.5)2=210.25and(51−35.5)2=240.25,
(28−35.5)2=56.25and(40−35.5)2=20.25,
(20−35.5)2=240.25.

Now that we have all the values, we add them together then divide them by how many there are, so
2.25+56.25+30.25+72.25+90.25+12.25+0.25+6.25+90.25+110.25+42.25+210.25+240.25+56.25+20.25+240.2516
=106416

=66.5

The last step is to take the square result of the previous result, called the variance , so:
√66.5≈8.155 is the standard deviation.

I hope I helped!

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