Question

The National Retail Federation commissioned a national survey in 2009. A

random sample of American adults were asked about their Christmas

shopping behavior. Among the 2597 respondents who said that they had

done some Christmas shopping that weekend, the average amount spent

was reported to be $343.31 and the standard deviation was $151.32

Use the appropriate confidence interval to test if the average amount spent that weekend was less that $350 at the alpha = .01 level. (use 4 decimal places for all calculations)

H_0: (mu or pi)  = $350

H_a: (mu or pi)  (=, <, >, or not equal to)  $350

SE =

Confidence Level =

MoE =  (Hint: for the appropriate t* look at the bottom of table III)

LB =

UB =

Based on this interval, do we reject or fail to reject the null hypothesis? (reject or fail to reject)

Answer 1

using excel>addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	151.32
Sample Mean	343.31
Sample Size	2597
Confidence Level	99%
Intermediate Calculations
Standard Error of the Mean	2.969342934
Degrees of Freedom	2596
t Value	2.5777
Margin of Error	7.6541
Confidence Interval
Interval Lower Limit	335.6559
Interval Upper Limit	350.9641

H_0: = $350

H_a:< $350

SE =2.9693

Confidence Level =99

MoE = 7.6541

LB =335.6559

UB =350.9641

fail to reject ho because 350 is inside the intervcal