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In: Statistics and Probability

A task force is studying the need for an additional bicycle path on a large university...

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.

Construct a 95% confidence interval for the population mean number of bicyclists using a bicycle path.

Solutions

Expert Solution

Solution :

Given that,

= 33

2 = 64

= 8

n = 7

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z/2* (/n)

= 1.960 * (8 / 7 ) = 6

At 95% confidence interval estimate of the population mean is,

- E < < + E

33 - 6 < < 33 + 6

27 < < 39

(27, 39)

orchestra answered 2 years ago
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