Question

A hospital administrator wants to determine the proportion of emergency room patients that use the emergency room (ER) for non-emergency care. She randomly samples records from 350 ER patients and determines that 74 of those patients required only non-emergency care.

1. The administrator constructs a 90% confidence interval for the true proportion of all ER patients who use the ER for non-emergency care. The error bound for the proportion EBP for this confidence interval is:

A. 0.036

B. 0.072

C. 0.030

D. 0.106

2. If the same data were used but the confidence level used was 95% instead of 90%, the error bound for the proportion EBP would be:

A. larger

B. the same

C. smaller

D. we are unable to determine unless another sample is obtained

3. What is meant by the term “95% confident” when constructing a confidence interval for a mean?

A. If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the true value of the population mean.

B. If we took repeated samples, the sample mean would equal the population mean in approximately 95% of the samples.

C. If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the sample mean.

D. If we took repeated samples, approximately 95% of the samples would produce the same confidence interval.

Answer 1

1)A. 0.036

2)A. larger

3)A. If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the true value of the population mean.

Explanation:

1) Let p=sample proportion of all ER patient who use for non emergency.

p=74/350

sample size n=350

Critical value Z_0.1/2=1.645

we know at 90% CI, margin of error=Z_0.1/2*

=0.036 approx

2)While 95% CI instead of 90% use, critical value will increase.So margin of error will also increase.

3) Remember population mean is a fixed value.If sample is many times our CI will include population mean 95% of times

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