Question

A group of GSU students in the Young Democrats Club wish to determine the likeability of their favorite candidate. They survey 2322 randomly selected registered voters and ask them to rate their candidate (on a “thermometer” from 0 to 100, where 0 means “very cold”and 100 means “very warm”feelings).

Suppose the sample of n=2322 responses have a mean warmth of 64.16 with a sample standard deviation of s=26.34.

Find the 95% confidence interval to estimate the population/national mean warmth rating for their candidate.

A) Note: The critical value, tc, that we use to calculate the margin of error for a 95% Confidence Interval is tc = ____ (round to 4 decimal places)

B) The margin of error for this confidence interval is: m = ____ (round to 4 decimal places)

C) The 95% Confidence Interval for the likeability of their candidate is: (____ , ____) round each to 2 decimal places

Answer 1

Solution :

t _/2,df = 1.9610

Margin of error = E = t_/2,df * (s /n)

=1.9610 * (26.34 / 2322)

Margin of error = E = 1.0719

The 95% confidence interval estimate of the population mean is,

- E < < + E

64.16 - 1.0719 < < 64.16 + 1.0719

63.0881 < < 65.2319

(63.09 , 65.23)