Question 6.5 : A simple random sample of 1,028 US adults in March 2013 found that 56% support nuclear arms reduction.4 Does this provide convincing evidence that a majority of Americans supported nuclear arms reduction at the 5% significance level?

The poll was of a simple random sample that includes fewer than 10% of US adults, meaning the observations are independent. In a one-proportion hypothesis test, the success-failure condition is checked using the null proportion, which is p0 = 0.5 in this context: np0 = n(1 - p0) = 1028 ⇥ 0.5 = 514 > 10. With these conditions verified, the normal model may be applied to pˆ.

summary(cars)

##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

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plot(cars)