Question 980413
The mpg data values are in <font color="red">red</font>. The other numbers in black are row numbers to keep track of all of the data in a neater form (compared to one long column of 45 values).


<table border=1><tr><th></th><th colspan="3">Mileage (mpg)</th></tr><tr><td>1</td><td><font color="red">21</font></td><td><font color="red">22</font></td><td><font color="red">20</font></td></tr><tr><td>2</td><td><font color="red">24</font></td><td><font color="red">22</font></td><td><font color="red">19</font></td></tr><tr><td>3</td><td><font color="red">16</font></td><td><font color="red">18</font></td><td><font color="red">25</font></td></tr><tr><td>4</td><td><font color="red">27</font></td><td><font color="red">14</font></td><td><font color="red">26</font></td></tr><tr><td>5</td><td><font color="red">13</font></td><td><font color="red">15</font></td><td><font color="red">14</font></td></tr><tr><td>6</td><td><font color="red">23</font></td><td><font color="red">13</font></td><td><font color="red">22</font></td></tr><tr><td>7</td><td><font color="red">18</font></td><td><font color="red">19</font></td><td><font color="red">26</font></td></tr><tr><td>8</td><td><font color="red">19</font></td><td><font color="red">18</font></td><td><font color="red">18</font></td></tr><tr><td>9</td><td><font color="red">19</font></td><td><font color="red">27</font></td><td><font color="red">16</font></td></tr><tr><td>10</td><td><font color="red">15</font></td><td><font color="red">22</font></td><td><font color="red">19</font></td></tr><tr><td>11</td><td><font color="red">16</font></td><td><font color="red">22</font></td><td><font color="red">21</font></td></tr><tr><td>12</td><td><font color="red">14</font></td><td><font color="red">15</font></td><td><font color="red">27</font></td></tr><tr><td>13</td><td><font color="red">24</font></td><td><font color="red">15</font></td><td><font color="red">24</font></td></tr><tr><td>14</td><td><font color="red">17</font></td><td><font color="red">26</font></td><td><font color="red">24</font></td></tr><tr><td>15</td><td><font color="red">27</font></td><td><font color="red">14</font></td><td><font color="red">20</font></td></tr></table>


n = 45 is the sample size. Since n > 30, we can use a standard normal distribution instead of the T distribution.


Use a calculator to find


sample mean: xbar = 19.911111
sample standard deviation: s = 4.378783
critical value: z = 2.326 (at 98% confidence)


Optionally, you can use a table like <a href="http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">this one</a> to find the critical z value. Look in the bottom "Z" row and above the "98%" confidence level to find z = 2.326

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The confidence interval is of the form (L,U) where L is the lower limit and U is the upper limit.


Lower Limit (L):
L = xbar - z*s/sqrt(n)
L = 19.911111 - 2.326*4.378783/sqrt(45)
L = 19.911111 - 2.326*0.652750429781364
L = 19.911111 - 1.51829749967145
L = 18.3928135003285
L = 18.39


Upper Limit (U):
U = xbar + z*s/sqrt(n)
U = 19.911111 + 2.326*4.378783/sqrt(45)
U = 19.911111 + 2.326*0.652750429781364
U = 19.911111 + 1.51829749967145
U = 21.4294084996715
U = 21.43


The 98% confidence interval for mu is (L,U) = <font size=5 color="red">(18.39, 21.43)</font> (rounded to 2 decimal places)


Side Note: the margin of error is approximately 1.51829749967145