In 1999, a sample of 400 in store shoppers showed that 184 paid by debit card. In 2013, a sample of the same size showed that 300 paid by debit card. Formulate the appropriate hypotheses to test whether the percentage of the debit card shoppers has increased. Carry out the test at the 0.01 significance level.
1. The problem involves:
a. Comparing the proportions of two populations
b. Comparing the variances of two populations
c. Comparing means of two independent populations
d. Comparing the means of two dependent samples
e. None of the above
2. What is the correct hypothesis setup for this problem?
a. H0: m2013 £ m1999 H1: m2013 > m1999
b. H0: m2013 ³ m1999 H1: m2013 < m1999
c. H0: p2013 £ p1999 H1: p2013 > p1999
d. H0: p2013 ³ p1999 H1: p2013 < p1999
e. None of the above
3. What is the sample proportion for 2013? ________ (round to 4 decimals)
4. What is the sample proportion for 1999? ________ (round to 4 decimals)
5. What is the combined proportion of success (who used debit card) for 1999 and 2013? _____ (round to 4 decimals)
Note: for questions #18 and #19, enter the data into the template in the order in which the years are presented on the hypotheses - that is, 2013 is first, then 1999 is second.
6. The computed test statistic for the sample above is ________. (round to 4 decimals).
7. At the 0.01 significance level, what is the critical value for testing the null hypothesis? _________ (round to 4 decimals)
8. What is the p-value for the test? _____________ (round to 4 decimals)
9. At the 0.01 significance level, what is the correct statistical conclusion?
a. Reject the null hypothesis
b. Fail to reject the null hypothesis
c. Reject the alternate hypothesis
d. Fail to reject the alternate hypothesis
e. None of the above. The test is inconclusive
10. Based on the result of the statistical test above, which of the following would be the correct conclusion?
a. The percentage of debit card users has increased from 1999 to 2013
b. The percentage of debit card users has decreased from 1999 to 2013
c. The percentage of debit card users has not changed from 1999 to 2013