Question

The government reported that 62% of tax returns were filed electronically in 2000. A random sample of 225 tax returns from 2002 was selected. From this sample, 163 returns were filed electronically. Construct a 95% confidence interval to estimate the actual proportion of taxpayers who filed electronically in 2002.

Q1a) what is the correct standard error for this scenario?

Q2) what is the correct confidence interval for the scenario?

Q3) is there enough evidence that this proportion has changed since 2000 based on thisample?

a) yes

b) no

c)not enough info

please answer all questions

I will thumbs up for correct answers in a timely manner

thanks

Answer 1

In the year 2002, point estimate of the proportion of taxpayers who filed electronically, = 163/225 = 0.7244

n = 225

Corresponding to 95% confidence interval, the critical z score = 1.96

1a) Standard error for this scenario = = 0.0298

2) Margin of error for the confidence interval = 1.96*0.0298

= 0.0584

Thus, the 95% confidence interval for this scenario

= (0.7244 - 0.0584, 0.7244 + 0.0584)

= (0.666, 0.783) = (66.6%, 78.3%)

3) Yes, there is enough evidence that this proportion has changed since 2000 bases on this sample since the lower limit of the confidence interval is greater than 62%.