In a random sample of 300 adults, 75 read a paper newspaper last week. Using z∗=1.96, find a 95% confidence interval for the proportion of all adults who did.
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Solution walkthrough1:59
The centre is the sample proportion: p^=30075=0.25.
Standard error: np^(1−p^)=3000.25⋅0.75=0.000625=0.025.
Margin of error: z∗ times the standard error, 1.96×0.025=0.049.
Go the margin each way from p^: 0.25−0.049=0.201 and 0.25+0.049=0.299.
Traps: 0.225 to 0.275 forgets z∗, 0.249 to 0.251 skips the root, 0.152 to 0.348 divides by 75.