Question

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.

Answer 1

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 = Z_0.02 = 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