You are asked to determine the estimated number of car accidents per month at a

Question

You are asked to determine the estimated number of car accidents per month at a specific intersection. Your report needs to be on your supervisor's desk the next morning. Since it is an estimate, your supervisor asked for an estimate with 98% confidence. In response to this assignment, you randomly selected a sample of 16 months over the last few years and compiled data on the number of car accidents that occurred during each of these months. The mean number of car accidents in these months was 42 per month with a sample standard deviation of 9 per month. What estimate will your report indicate? 9)

Explanation / Answer

Since it has been stated that the confidence ineterval is 98% and you are measuring the range of the avg accidents we are concerned for the boundries of 1% each on lower and upper tail.

So from the z table check for the values of z which has probability/area under the curve as 0.01 & 0.99 (for 1% each side)

we get z = -2.33 and z=2.33 respectively for 1% on lower and upper tail

Substitutuing the same in the equation

z= (X'-mu)/(sd/sqrt(n))

where we have mu = 42

n=16

sd = 9

so.,

X'= mu + z*(sd/sqrt(n)

so., LCL = 42 -2.33 *9/sqrt(16) =36.7575

& UCL = 42 + 2.33 * 9/sqrt(16) = 47.2425

And so here we can say that the mean accidents which we can report for 98% conf interval is 36.7575 to 47.2425

Hope the above response has helped you in understanding the problem. Pls. upvote if it has really helped you. Good Luck!!

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