The 2009 holiday retail season, which kicked off on November 27, 2009 (the day after Thanksgiving), had been marked by somewhat lower self-reported consumer spending than was seen during the comparable period in 2008. To get an estimate of consumer spending, 436 randomly sampled American adults were surveyed. Daily consumer spending for the six-day period after Thanksgiving, spanning the Black Friday weekend and Cyber Monday, averaged \(\$ 84.71\). A \(95 \%\) confidence interval based on this sample is \((\$ 80.31, \$ 89.11)\). Determine whether the following statements are true or false, and explain your reasoning.

(a) We are \(95 \%\) confident that the average spending of these 436 American adults is between \(\$ 80.31\) and \(\$ 89.11\).

(b) This confidence interval is not valid since the distribution of spending in the sample is right skewed.

(c) \(95 \%\) of random samples have a sample mean between \(\$ 80.31\) and \(\$ 89.11\).

(d) We are \(95 \%\) confident that the average spending of all American adults is between \(\$ 80.31\) and \(\$ 89.11\).

(e) A \(90 \%\) confidence interval would be narrower than the \(95 \%\) confidence interval.

(f) The margin of error is 4.4.

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