Question

In: Math

Urban planners in Melbourne average 10.2 years’ experience. We know this from a Census of urban...

  1. Urban planners in Melbourne average 10.2 years’ experience. We know this from a Census of urban planners, but the raw data was lost, so we cannot use the data to compute σ. What an inconvenience!    (a) In a random sample of 65 urban planners in Melbourne’s growth areas, the average was 8.7 years with a standard deviation of 0.52. Are growth-areas planners significantly less experienced than the metropolitan average? Presume alpha = 0.05 (b) The same sample of urban planners reports an annual salary of $25,665 with s=$722. The statewide average salary is $23,899. Is there statistical evidence to suggest that growth area planners salaries are significantly higher than Melbourne overall? Presume alpha = 0.05

Solutions

Expert Solution

a) H0: > 10.2

H1: < 10.2

The test statistic t = ()/(s/)

= (8.7 - 10.2)/(0.52/)

= -23.26

At alpha = 0.05, the critical value is t0.05, 64 = -1.669

Since the test statistic value is less than the critical value (-23.26 < -1.669), so we should reject the null hypothesis.

Yes, at 0.05 significance level we can conclude that growth-areas planners significantly less experienced than the metropolitan average.

b) H0: < 23899

H1: > 23899

The test statistic t = ()/(s/)

= (25665 - 23899)/(722/)

= 19.72

At alpha = 0.05, the critical value is t0.95, 64 = 1.669

Since the test statistic value is greater than the critical value (19.72 > 1.669), so we should reject the null hypothesis.

At 0.05 significance level there is sufficient evidence to conclude that growth area planners salaries are significantly higher than Melbourne overall.


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