Question

# An increase in the rate of consumer savings is frequently tied to a lack of confidence...

An increase in the rate of consumer savings is frequently tied to a lack of confidence in the economy and is said to be an indicator of a recessional tendency in the economy. A random sampling of

n = 290

savings accounts in a local community showed a mean increase in savings account values of 7.4% over the past 12 months, with a standard deviation of 5.6%. Estimate the mean percent increase in savings account values over the past 12 months for depositors in the community.

%

Find the 95% margin of error (in %) for your estimate. (Round your answer to three decimal places.)

%

Solution :

Given that,

Point estimate = sample mean = = 0.074

sample standard deviation = s = 0.056

sample size = n = 290

Degrees of freedom = df = n - 1 = 290 - 1 = 289

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,289 = 1.968

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

= 1.968 * (0.056 / 290)

Margin of error = E = 0.006

Margin of error = E = 0.6%