1. Section 7.2 Estimating  When  Is Unknown

2. 2 - Usually, when  is unknown,  is unknown as well. - So use the sample standard deviation s to approximate . - Sampling distribution for x changes from a normal z to a student’s t distribution.

3. 3 Student’s t Distribution - History -discovered in 1908 by W. S. Gosset. -employed as a statistician by Guinness brewing company (discouraged publication of research by its employees) -published his research under the pseudonym Student. -first to develop a statistical method for obtaining reliable information from samples of populations with unknown .

4. 4 no z-score but a t-score! Assume distribution of x is normal…

5. 5 Student’s t Distribution

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7. 7 P (–t c  t  t c ) = c Use t c = invT(%, d.f.) (under 2 nd vars) 99% confident and n = 5 For 90% confidence find z c 90% confident and n = 9 then for n = 100

8. 8 Margin of Error when  unknown

9. 9 Check if x is normal, if not, check for n > 30. And random sample T interval when  Is Unknown

10. 10 Ex: 1 Seven fossil skeletons from a species of horse. shoulder heights in cm (assume normal): 45.3 47.1 44.2 46.8 46.5 45.5 47.6 x  46.14 and s  1.19 Find a 99% confidence interval for , mean shoulder height of the entire species.

11. 11 T Interval in calc. STAT  TESTS  #7 Zinterval  choose STATS (unless you are given actual data…in which case enter it in L1 and choose DATA)  Enter x-bar, s, n, c-level  Calculate

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13. 13 So z or t??? Depends on how much you know about x distribution First: Normal? Not normal, but n > 30? Assume random, even if not stated Second:

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