Question

In: Statistics and Probability

Of 50 bank customers depositing a check, 17 received some cash back. (a) Construct a 90...

Of 50 bank customers depositing a check, 17 received some cash back.

(a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)

The 90% confidence interval is from to

Expert Solution

Solution :

Given that,

n = 50

x = 17

Point estimate = sample proportion = = x / n = 17/50=0.34

1 - = 1- 0.34 =0.66

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E Z/2 * $\sqrt$ (( * (1 - )) / n)

= 1.645 * $\sqrt$ ((0.34*0.66) / 50)

E = 0.1102

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.34-0.1102 < p <0.34+ 0.1102

0.2298< p < 0.4502

The 90% confidence interval for the population proportion p is : 0.2298, 0.4502

orchestra answered 2 years ago

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