Question

1. How long does it take an ambulance to respond to a request for emergency medical aid? One of the goals of one study was to estimate the response time of ambulances using warning lights (Ho & Lindquist, 2001). They timed a total of 67 runs in a small rural county in Minnesota. They calculated the mean response time to be 8.51 minutes, with a standard deviation of 6.64 minutes. Calculate a 95% confidence interval for the mean for this set of data.

1. State the desired level of confidence.
2. Calculate the confidence interval and confidence limits.
   • (1) Calculate the standard error of the mean (s¯¯¯X).(sX¯).
   • (2) Calculate the degrees of freedom (df ) and identify the critical value of t.
   • (3) Calculate the confidence interval and confidence limits.
3. Draw a conclusion about the confidence interval.

a 95% confidence interval was constructed for N = 67 ambulance runs. Assuming the mean and standard deviation remained the same (¯¯¯X=8.51,s=6.64)…(X¯=8.51,s=6.64)…

1. What is the confidence interval for the mean for N = 125 ambulance runs rather than 67?
2. What is the confidence interval for the mean for N = 33 ambulance runs rather than 67?
3. How do these two confidence intervals compare with the 95% confidence interval of (6.89, 10.13) calculated in Exercise 8?

2. For each of the following situations, calculate a 95% confidence interval for the mean (σ known), beginning with the step, “Identify the critical value of z.”

1. ¯¯¯X=50.00,σ¯¯¯X=3.00

Answer 1

1:

(a)

The desired level of confidence is 0.95

(b)

(C)

We are 95% confident that true mean response time is lie in the above interval.

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For n = 125:

For n = 33:

(c)

As the sample increases confidence interval becomes narrower.

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