High School

A bank wants to estimate the difference in the proportion of its "big" customers who have a second account with a different bank and the proportion of its "small" customers who also have an account with another bank. Of the 200 "big" customers randomly selected, 160 claimed to also bank elsewhere. Of the 300 "small" customers randomly selected, 120 claimed to also bank with other banks. Check the conditions for constructing a confidence interval for the difference in proportions.

A. Random condition: met
10% condition: met
Large Counts condition: met
All conditions for inference are met.

B. Random condition: not met
10% condition: met
Large Counts condition: met
All conditions for inference are not met.

C. Random condition: met
10% condition: does not apply
Large Counts condition: met
All conditions for inference are met.

D. Random condition: met
10% condition: met
Large Counts condition: not met
All conditions for inference are not met.

Answer :

Final answer:

The conditions for constructing a confidence interval for the difference in proportions are met.

Therefore, all conditions for inference are met, and a confidence interval for the difference in proportions can be constructed.

Explanation:

The conditions for constructing a confidence interval for the difference in proportions in this case are as follows:

  1. Random condition: met - The 200 "big" customers and 300 "small" customers were randomly selected.
  2. 10% condition: met - The sample size of 200 and 300 customers is less than 10% of the total population.
  3. Large Counts condition: met - The number of successes and failures in the samples (160 and 120) are both greater than 10.

Therefore, all conditions for inference are met, and a confidence interval for the difference in proportions can be constructed.

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