| | | (1) 95% confidence interval |
| | | sample of size 76, 41 people believed |
| | | n=76, x=41 |
| | | p =41/76= 0.5395 |
| | | 95% interval =
(p ̅- Z_(α/2) √((p ̅*(1-p ̅))/n), p ̅+ Z_(α/2) √((p ̅*(1-p ̅))/n)) |
| | | 95% confidence level Zα/2 = 1.96 |
| | | 95% confidence interval as (0.5395-1.96*√((0,5395*(1-0.5395))/76) , 0.5395+1.96*√((0,5395*(1-0.5395))/76) ) = (0.4274, 0.6515). |
| | | Null Hypothesis H0: people who believe is less than/equal 0.5. H0: p ≤ 0.5 (Upper tail) |
| | | Alternative greater than 0.5. H1: p > 0.5 (claim) |
| | | α =0.05 |
| | | Z = |
| | | Zα =1.645 region Z > 1.645 |
| | | Substituting the value Z = (((41/76)-0.5))/√((0.5(1-0.6))/76) =0.688 |
| | | (2) 95% sample of size 76, 40 people keep up with space exploration events |
| | | n=76, x=40 |
| | | =40/76= 0.5263. The 95% |
| | | confidence people who keep up: |
| | | (, |
| | | standard deviation: |
| | | Zα/2 = 1.96 |
| | | (0.5263-1.96* , 0.5263+1.96* ) = (0.4141, 0.6386) |
| | | null hyp: less than or equal to 0.5. H0: p ≤ 0.5 (Upper tail) |
| | | alternative: greater than 0.5. H1: p > 0.5 (claim)
Significance level α =0.05
Test statistic Z = ((p ̅-p))/√((p(1-p))/n) follows a standard normal distribution
|
| | | Zα =1.645 region Z > 1.645 |
| | | sub Z = (((40/76)-0.5))/√((0.5(1-0.6))/76) =0.4588 |
jolevo
week_9_assignment.xlsx
