In: Statistics and Probability
The wedding of Prince Harry and Meghan Markle was held on May 19, 2018, in St. George’s Chapel at Windsor Castle in the United Kingdom. Prince Harry is a member of the British royal family, and Meghan Markle is an American actress. Their wedding ceremony was broadcast worldwide. A random sample of 500 British citizens was asked if they watched Harry and Meghan’s wedding, and 42% of those sampled replied that they did watch the wedding ceremony. Use this data to calculate and interpret a 96% confidence interval for the proportion of all British citizens who watched Prince Harry and Meghan Markle’s wedding ceremony.
Solution :
Given that,
n = 500
Point estimate = sample proportion = = 42% = 0.42
1 - = 1 - 0.42 = 0.58
At 96% confidence level
= 1 - 96%
=1 - 0.96 =0.04
/2
= 0.02
Z/2
= Z0.02 = 2.054
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.054 (((0.42 * 0.58) / 500 )
= 0.045
A 96% confidence interval for population proportion p is ,
± E
= 0.42 ± 0.045
= ( 0.375, 0.465 )
We are 96% confident that the true proportion of all British citizens who watched Prince Harry and Meghan Markle’s wedding ceremony between 0.375 and 0.465