Answer
i) We would expect that the number of parents who spank their children is 824.
ii) The results of the survey have suggested that the attitude towards spanking has changed. This is because an observation of 781 parents who spank their kids would be unusual, assuming that 80% of parents still spank their kids. (781 is more than 2 standard deviations away from the mean).
Work Step by Step
If we assume parent’s attitude towards spanking hasn’t change since 1995 then we assume that 80% of parents still spank their children.
i ) The expected value of parents who spank = np
np
= 0.80 x 1030
= 824
We would expect that the number of parents who spank their children is 824.
ii) Standard deviation
$\sqrt {np(1-p)}$
= $\sqrt {1030 \times 0.80 \times (1-0.80)}$
= 12.83744523
$\approx$ 12.837
Determine whether 781 is an unusual value
μ−2σ = 824 - 2(12.837) = 798.326
μ+2σ = 824 + 2(12.837) = 849.674
781 is an unusual value because it does not fall between 798.326 and 849.874.
