Question

A random sample of 2597 adult Americans in November 2009 revealed a sample mean of $ 343.31 that was spent on Christmas shopping over the Thanksgiving weekend a. Is $ 343.31 a parameter or a statistic? What symbol is used for this? The value $ 343.31 is a The symbol used is b. Determine the value of for a 95% confidence interval for the population mean amount spent on Christmas shopping over that weekend. c. What further information about the sample data do you need to determine this confidence interval? d. Determine the endpoints of this confidence interval the sample standard deviation turned out to be $250. Then repeat, assuming that the sample standard deviation turned out to be $300

Answer 1

a) The value $ 343.31 is a statistic. The symbol used is $\bar x$

b) t^* = 1.961

c) Sample standard deviation

d) For Standard deviation = $250

The 95% confidence interval is

*/ Z

250 = 343.31±1.961- v2597

= 343.31±9.62

= 333.69.352.93

For Standard deviation = $300

The 95% confidence interval is

*/ Z

300 = 343.31±1.961- v2597

= 343.31±11.54

=331.77,354.85

e) These intervals are centered at the sample mean. The interval created with larger standard deviation is wider.