Try the fastest way to create flashcards
Question

# The data in previous exercise follow a Normal distribution quite closely except for one patient with HAY angle 50 degrees, a high outlier. Data available below.(a) Find the 95% confidence interval for the population mean based on the 37 patients who remain after you drop the outlier.(b) Compare your interval in (a) with your interval from previous exercise. What is the most important effect of removing the outlier? In general, you shouldn't remove an outlier unless you have reason to believe it is an error or unless you are interested only in "typical" cases. For a more in-depth discussion of how to handle outliers in various situations, read the discussion on outliers in previous chapters.28 32 25 34 38 26 25 18 30 26 28 13 2021 17 16 21 23 14 32 25 21 22 20 18 2616 30 30 20 50 25 26 28 31 38 32 21

Solution

Verified
Step 1
1 of 3

(a) The mean is the sum of all values divided by the number of values:

$\overline{x}=24.7568$

The variance is the expected value of the squared deviation from the mean. The standard deviation is the square root of the variance.

$s=6.3395$

The degrees of freedom is the sample size decreased by 1.

$df=n-1=37-1=36>30$

The critical t-value is the value in the row with $df=30$ and in the column with confidence level 95% of table C:

$t^*=2.042$

The confidence interval is:

$\overline{x}-t_{\alpha/2}\cdot \dfrac{s}{\sqrt{n}}\text{ to }\overline{x}+t_{\alpha/2}\cdot \dfrac{s}{\sqrt{n}}$

Fill in the known values:

$24.7568-2.042\cdot \dfrac{6.3395}{\sqrt{37}}\text{ to }24.7568+2.042\cdot \dfrac{6.3395}{\sqrt{37}}$

Simplify:

$22.6286\text{ to }26.8850$

## Recommended textbook solutions #### Probability and Statistics for Engineers and Scientists

9th EditionISBN: 9780321629111 (4 more)Keying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers
1,204 solutions #### The Practice of Statistics for the AP Exam

5th EditionISBN: 9781464108730 (1 more)Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor
2,433 solutions #### Statistics and Probability with Applications

3rd EditionISBN: 9781464122163Daren S. Starnes, Josh Tabor
2,555 solutions #### The Practice of Statistics in the Life Sciences

3rd EditionISBN: 9781464175367Brigitte Baldi, David Moore
945 solutions