Question

A task force is studying the need for an additional bicycle path on a large university campus. It is assumed that the distribution of bicyclists using a path between classes is normally distributed with a population variance of about 64. A random sample of 7 existing bicycle paths showed that the sample mean number of bicyclists using a path between classes was 33.

A group of interested students took its own sample of 5 different bicycle paths, and computed a confidence interval for the population mean that ranged from (16.0 , 25.173 ). What is the probability content (or the level of confidence) of this interval?

Answer 1

Solution:

    Given : The distribution of bicyclists using a path between classes is normally distributed with a population variance of about 64.

Population Variance =

Then population standard deviation =

Sample size = n = 5 and computed a confidence interval for the population mean that ranged from (16.0 , 25.173 ).

We have to find the probability content (or the level of confidence) of this interval.

Lower Limit =

Upper limit =

Subtract lower limit from upper limit , we get :

               

           _    - - -

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           0     + 2 E = 9.173

                         E   =   9.173 / 2

                        E    = 4.5865

Now use following formula:

That is z = 1.28

Now look in z table for z = 1.2 and .08 and find corresponding area:

Area = 0.8997 corresponds to 1.2 and 0.08

That is approximately 0.90

So area below z = 1.28 is 0.90

Thus level of confidence = 0.80 or 80% .