Question 9 A finance officer for a large company wants to find out an estimate for the percentage of company accounts whose payments are more than 30 days overdue. He carries out a survey by randomly selecting a sample of accounts. The results are shown in the table below. Number of days overdue Less than 10 days Between 10 and 30 days More than 30 days Number of accounts 80 28 42 a) Use the information in the table above to find the percentage of accounts in the sample that are more than 30 days overdue. b) Using your answer to part a), find the 90% confidence interval for the percentage of all the accounts in the company that are more than 30 days overdue. Give your answers to the nearest integer. c) The finance officer wants the total width of the 90% confidence interval in part b) to be less than 8%. Work out the smallest sample size that should be taken to achieve this.

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Question 9
A finance officer for a large company wants to find out an estimate for the percentage of
company accounts whose payments are more than 30 days overdue. He carries out a
survey by randomly selecting a sample of accounts. The results are shown in the table
below.
Number of days overdue
Less than 10 days
Between 10 and 30 days
More than 30 days
Number of accounts
80
28
42
a) Use the information in the table above to find the percentage of accounts in the
sample that are more than 30 days overdue.
b) Using your answer to part a), find the 90% confidence interval for the percentage
of all the accounts in the company that are more than 30 days overdue.
Give your answers to the nearest integer.
c) The finance officer wants the total width of the 90% confidence interval in part b)
to be less than 8%. Work out the smallest sample size that should be taken to
achieve this.
Transcribed Image Text:Question 9 A finance officer for a large company wants to find out an estimate for the percentage of company accounts whose payments are more than 30 days overdue. He carries out a survey by randomly selecting a sample of accounts. The results are shown in the table below. Number of days overdue Less than 10 days Between 10 and 30 days More than 30 days Number of accounts 80 28 42 a) Use the information in the table above to find the percentage of accounts in the sample that are more than 30 days overdue. b) Using your answer to part a), find the 90% confidence interval for the percentage of all the accounts in the company that are more than 30 days overdue. Give your answers to the nearest integer. c) The finance officer wants the total width of the 90% confidence interval in part b) to be less than 8%. Work out the smallest sample size that should be taken to achieve this.
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