Question

How much money do people spend on graduation gifts? In 2007, a federation surveyed 2215 consumers who reported that they bought one or more graduation gifts that year. The sample was selected in a way designed to produce a sample representative of adult Americans who purchased graduation gifts in 2007. For this sample, the mean amount spent per gift was $55.25. Suppose that the sample standard deviation was $20. Construct a 98% confidence interval for the mean amount of money spent per graduation gift in 2007. (Round your answers to three decimal places.) PLEASE EXPLAIN IN STEPS

(_,_)

Interpret the interval.

We are confident that the mean amount of money spent per graduation gift in 2007 was within this interval 98% of the time.

We are confident that 98% of the amount of money spent per graduation gift in 2007 was within this interval.   

  We are 98% confident that the mean amount of graduation money spent was within this interval.

We are 98% confident that the mean amount of money spent per graduation gift in 2007 was within this interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 55.25

sample standard deviation = s = 20

sample size = n = 2215

Degrees of freedom = df = n - 1 = 2215 - 1 = 2214

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

t/2,df = t0.01,2214 = 2.328

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

= 2.328 * (20 / 2215)

Margin of error = E = 0.989

The 98% confidence interval estimate of the population mean is,

  ± E  

= 55.25 ± 0.989

= ( 54.261, 56.239 )

We are 98% confident that the mean amount of money spent per graduation gift in 2007 was within this interval.