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A credit card company is interested in investigating spending differences for its cardholders between December and...

A credit card company is interested in investigating spending differences for its cardholders between December and January (they believe cardholders are likely to spend more money in December due to holiday shopping). A random sample of 20 cardholders is selected, and the amount charged to their credit card in December 2014 and January 2015 is recorded. The data collected is summarized in the table below.

Difference n yd sd
Dec - Jan 20 237.325 136.5093

Estimate the mean difference in charges between the two months using 99% confidence.

  • We plan to estimate the mean difference using the following formula: ¯yd±t(sd√nd)y¯d±t(sdnd) . Explain why this is the appropriate formula to use.
    • Charges in the two months were recorded for the same 20 cardholders.
    • All the individuals sampled had the same type of credit card.
    • All the individuals sampled had credit charges recorded.
    • The data should not be treated as paired.
  • Using the table below, the appropriate t-critical point for this interval would be t =  
  • Calculate the confidence interval: Lower limit =    Upper limit =    (Round to 4 decimal places.)
  • Which of the following conclusions is correct for the interval calculated?
    • With 99% confidence, we estimate the mean amount charged to this credit card by all cardholders in December is less than the mean charged in January by some amount between the limits calculated above.
    • With 99% confidence, we conclude there is not a significant difference in the mean amount charged to this credit card by all cardholders in December & January.
    • With 99% confidence, we estimate the mean amount charged to this credit card by all cardholders in December is more than the mean charged in January by some amount between the limits calculated above.
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Answer #1

The values given in ydbar and sd have no gaps. I believe taken values in answer are correct.

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