Question

4. In a survey, 1,858 out of 2600 voters said they expected declining economic conditions to continue for the next 12 months. This is a measure of consumer confidence.
   1. Construct a 99 percent confidence interval for the proportion of respondents who believe there will be "hard (declining) times" in the next 12 months.
   2. Consumer confidence is an indicator for economic expansion and growth. What do these findings indicate for economic growth?

Answer 1

a)Proportion of people who expect economic condition to continue declining for next 12 months (p) = 1858/2600

= 0.715

Hence, proportion of people who don't expect economic condition to continue declining for next 12 months (q) = 1-p

= 1- 0.715

= 0.285

Hence, 99% confidence interval for proportion of people who expect economic condition to continue to decline for next 12 months (p) will be given by: CI = [ p-z*√(p*q)/n, p+z*√(p*q)/n] ,

where z is the critical value of standard normal variate at a/2 and a is the level of significance = 1-0.99 =0.01

So, critical value of z at 0.01/2 = 2.576

n is the sample size =2600

Therefore, CI = [ 0.715-2.576*√(0.715*0.286/2600), 0.715+2.576*√(0.715*0.285/2600)]  

= [0.71476, 0.71523]

Confidence interval is narrow which indicates higher accuracy

b) Hence consumer confidence is about 71% which suggest there will be declining economic growth in next 12 months.