6. With online grocery shopping popularity increasing, has there been a significant increase in the proportion of credit cards used to buy groceries based on the historical 35% of cardholders who at least sometimes used their cards to buy groceries? (Use .???????=0.05)

a. Write out the null and alternative hypothesis using correct notation.

b. Calculate the value of the test statistic and use this to make the decision of the test.

c. Interpret your results in the context of the question.

d. Show that the necessary conditions hold for this test to be valid

e. Given your decision, what type of error (Type 1 or 2) could you have possibly made?

Use their cards sometimes to buy Groceries (Palkhi Kapadia) Cumulative Frequency Percent Percent Valid Often 127 14.94% 14.94% Sometimes 193 22.71% 37.65% Never 530 62.35% 100.00% Total 850 100.00%