1. A previous study gave (0.27, 0.44) as a confidence interval for p. Find the minimum sample size required to ensure that your estimate ( ˆ p ) will be within 0.09 of p with 99% confidence. IMPORTANT: Use a critical value that you found with your calculator (not from a table), and round it to 3 places after the decimal point before you plug it into a formula and perform your calculations. Do not round-off any other intermediate results. n = 3.
2.
(a) For a confidence level of 96%, find the critical value z?/2z?/2. Round your answer to 2 places after the decimal point.
z?/2=z?/2=
(b) For a confidence level of 95% and a sample size of 6, find the critical value t?/2t?/2. Round your answer to 3 places after the decimal point.
t?/2=
3. The two data sets in the table below are dependent random samples. The population of (x?y)(x-y) differences is approximately normally distributed.
| x | 56 | 54 | 53 | 62 | 63 | 59 | 51 |
|---|---|---|---|---|---|---|---|
| y | 34 | 32 | 39 | 37 | 30 | 28 | 40 |
For all three parts below, round your answers to 3 places after the decimal point, if necessary
(a) Find the value of ¯dd¯ .
¯d=d¯=
(b) Find the value of sd.
sd =
(c) Construct a 95% confidence interval for the mean difference. If it is not appropriate to construct a confidence interval in this situation, then enter "0" in both answer boxes below.
95% confidence interval: ( , )
Thank you so much in advance!