Question

Mars migration ~ Living on Mars would be a dream come true for many Americans after popular movies such as Total Recall, The Martian and John Carter, which are based on Mars. To gauge public interest, a nationwide survey conducted by SpaceX on whether people would like to live on Mars found that 772 out of 1,064 randomly selected Americans would indeed like to live on Mars.

Using this data, Douglas wants to estimate the actual proportion of Americans who would like to live on Mars.

What is the lower bound for a 90% confidence interval? Give your answer to 4 decimal places.

Answer 1

Solution :

n = 1064

x = 772

= x / n = 772/ 91064 = 0.725

1 - = 1 - 0.275 = 0.275

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 * (((0.725 * 0.275 ) / 1064)

= 0.0225

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.725 - 0.0225

=0.7025

The lower bound = 0.7025