Question

Measurement of the waiting time of 24 randomly selected patients at a hospital emergency room gave mean and sample standard deviation 11.3 and 6.5 minutes. Assume that the waiting times are normally distributed. 2. A 95% confidence interval for the mean waiting time of all patients is about (a) 11.3+(1.645)(*) (b) 11.3+(1.96)() (c) 11.3 (1.714)() (d) 11.3 (2.069) (e) 11.3 + (2.575)() 3. II, after you obtain the confidence interval, you find it to be too wide, which of the following remedial steps can you take to reduce the width of the confidence interval? 1. To construct a 90% confidence interval instead of a 95% one. II. To construct a 99% confidence interval instead of a 95% one. III. To re-do the 95% confidence interval with only a half of the sample data. (a) I only (b) Il only (c) III only (d) I and III only (e) II and III only (d(

Answer 1

To calculate a 95% confidence interval for the mean waiting time, the student should use option (b) 11.3 + (1.96)*(6.5 / sqrt(24)). To reduce the width of the confidence interval, the student can choose option (d) I and III only.

Step-by-step explanation:

To calculate a 95% confidence interval for the mean waiting time, we need to use the formula:

CI = mean +/- (critical value * standard deviation / sqrt(n))

Where:

- CI represents the confidence interval

- mean is the sample mean waiting time

- critical value is the value from the t-distribution table for a 95% confidence level and (n-1) degrees of freedom

- standard deviation is the sample standard deviation

- n is the sample size

In this case, the student should use option (b) 11.3 + (1.96)*(6.5 / sqrt(24)) to calculate the 95% confidence interval.

To reduce the width of the confidence interval, the student can choose option (d) I and III only. This means constructing a 90% confidence interval instead of a 95% one and re-doing the 95% confidence interval with only half of the sample data.