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1 Sectio 10 Aswer Key: % 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 1) A simple radom sample of New Yorkers fids that 87 are left-haded. (a) Fid the 95% cofidece iterval for the proportio of New Yorkers who are left-haded. p = 87 = p ± z = ± ± = (0.0695,0.1045) We are 95% cofidet that the proportio of New Yorkers who are left-haded is with a margi of error of (b) Fid the 99% cofidece iterval: p ± z = ± ± = ( , ) We are 99% cofidet that the proportio of New Yorkers who are left-haded is with a margi of error of (c) We ca be 99.9% cofidet that the proportio of New Yorkers who are left-haded is betwee what two umbers? p ± z = ± ± = (0.0577,0.1163) We are 99.9% cofidet that the proportio of New Yorkers who are left-haded is with a margi of error of (d) Either our group of is amog the 10% most uusual samples, or the proportio of New Yorkers who are left-haded is betwee what two umbers?

3 p ± z = 0.84 ± ± = (0.780,0.900) (c) Either our sample of 250 orders was amog the 5% most uusual, or p is betwee what two umbers? This is a 95% cofidece iterval: p ± z = 0.84 ± ± = (0.795,0.885) 4) I our effort to fid out what percetage of all statistics are meaigless, we do a well-fuded study ad lear that of 420 examied statistics, 386 of them were meaigless. Fid a 99.5% cofidece iterval for the true proportio of all statistics that are meaigless. p = = ( ) p ± z = ± ± = (0.882,0.956) 5) The U.S.R.S. (Uio of Starfleet Red Shirts) wats to kow the probability of a Red Shirt dyig whe he beams dow to a plaet with Captai Kirk. Fid a 99.8% cofidece iterval for this probability, after learig that 35 of the last 93 Red Shirts who beamed dow with Kirk met a ufortuate ed. p = = ( ) p ± z = ± ± = (0.221,0.531) 6) A radom sample of 1021 adults foud that 38% said they believe i ghosts. Fid a 90% cofidece iterval for the percetage of all adults who believe i ghosts. Fid a 99% cofidece iterval. p = (1 0.38) p ± z = 0.38 ± ± = (0.3545,0.4055) 0.38(1 0.38) p ± z = 0.38 ± ± = (0.341,0.419)

5 (b) Suppose we wat to cut the margi of error dow to 4%. How may? = ( z 2 m ) p(1 p) = ( ) 0.25(1 0.25) = 317.1, so = 318. (rememberig that we have to roud up to the smallest acceptable sample size). (c) Dow to 3% how may? = ( z m )2 p(1 p) = ( ) (1 0.25) = 563.8, so = 564.

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