Bank acquisitions. Refer to Exercise 6.3 (page 317) (a) Find , the standard error of . (b) Give the 95% confidence interval for p in the form of estimate plus or minus the margin of error. (c) Give...

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Bank acquisitions. Refer to Exercise 6.3 (page 317)


(a) Find
, the standard error of.


(b) Give the 95% confidence interval for p in the form of estimate plus or minus the margin of error.


(c) Give the confidence interval as an interval of percents.



Exercise 6.3


Bank acquisitions. The American Bankers Association Community Bank Competitiveness Survey had responses from 760 community banks. Of these, 283 reported that they expected to acquire another bank within five years.


(a) What is the sample size n for this survey?


(b) What is the count X of community banks that expect to acquire another bank?


(c) Find the sample proportion
.




Answered Same DayDec 25, 2021

Answer To: Bank acquisitions. Refer to Exercise 6.3 (page 317) (a) Find , the standard error of . (b) Give the...

David answered on Dec 25 2021
123 Votes
95% Confidence Interval for p
p̂ = x
n
= 283760 = 283/760 ≈ 0.372368 ≈ 0.372
Significance level
= α = 1− confidence = 1 − 0.95 = 0.05
Critical z-value = zα/2 = z0.05/2 = z0.025 = 1.96 (From z table)
Standard error of p̂ : SE =

p̂× (1 − p̂)
n
=

283/760 × 477/760
760 ≈ 0.017536
SEp̂...
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