a. Calculate the 95% confidence interval for the proportion of Standard type cards with rewards points and interpret the confidence interval in context. Show your workings and write out the confidence interval using the correct notation.

b. Show that the necessary condition/s hold for this confidence interval to be valid.

c. What is the margin of error of the 95% confidence interval estimate for the proportion of

Standard type cards with rewards points?

d. Calculate the sample size required to estimate the proportion of Standard type cards with

rewards points with 95% confidence and a margin of error of 2%?

Rewards * Type Crosstabulation (Palkhi Kapadia) Type Gold Standard Low Interest Total Rewards No Count 30 298 78 406 % within Type 38.5% 42.9% 100.0% 47.8% Yes Count 48 396 0 444 % within Type 61.5% 57.1% 0.0% 52.2% Total Count 78 694 78 850 % within Type 100.0% 100.0% 100.0% 100.0%Descriptive: of a m condence Interval for the average monthly credit card balance Statistic Std. Error 01.02330 037.237 51350.09 81,007.00 51.030.00 1170591304 01.005.030 80.200 50.050 .004 .1 00