8.1
Using 
, the sample proportion, 
= 11/40 = 0.275,
with SE=0.0706. The 95% interval is 0.275+1.96(0.0706) = 0.1366 to
0.4134. Using the Wilson estimate, 
= 13/44 =
0.2955, with SE=0.07214. The 95% interval is 0.2955+1.96(0.07214) =
0.1606 to 0.4303.
8.2
Using 
, the sample proportion, 
= 487/811 = 0.600, with SE=0.0172. The 99%
interval is 0.600+2.576(0.0172) = 0.5562 to 0.6448. Using the Wilson
estimate, 
= 489/815 = 0.6,
with SE=0.0172. The 99% interval is 0.6+2.576 (0.0172) = 0.5558 to
0.6442.
8.9
Using 
, the sample proportion, 
= 185/200 =
0.925, with SE=0.018625. The 95% interval is 0.8885 to 0.9615. Using the Wilson
estimate, 
= 187/204 =
0.9167, with SE=0.01954. The 95% interval is 0.8787 to 0.9546.
8.12
(a) H0: p = 0.2 vs. Ha: p > 0.2. It is a one-sided
alternative because we are only interested in the case where more than 20% are
willing to buy. (b) Using 
, the sample proportion, 
= 11/40 = 0.275,
with SE=0.0706. Z = (0.275-0.20)/0.0706 = 1.0623. The p-value is 0.145. Using
the Wilson estimate, 
= 13/44 = 0.295,
with SE=0.0721. Z=1.323 and the p-value is 0.093. Using the Wilson estimate,
this data is significant at the 10% level, but only barely. This is rather weak
evidence that more than 20% will buy the product.
8.16 n=(1.96/0.03)2 (0.44)(0.56) = 1051.7, so use 1052.
8.20 (a) Since 19 preferred instant coffee, we assume the other 31 preferred freshly brewed. The sample proportion is 0.62, with a SE of 0.06864. The Z statistic is 1.748 and the one-sided p-value is 0.04. This is significant at 5%. We conclude that this is strong evidence that freshly brewed is preferred over instant. (b) The 90% interval is 0.5071 to 0.733. This shows that there is a chance that the ÒmajorityÓ could be as slim as a bare 51% of the population.
8.24 Sample size n = (1.96/0.06)2 (0.40)(0.60) = 256.1. Might want to round this up to 257.