ll be profitable if the average wind speed at the proposed turbine site is more than 8 mph. For a site north of West Lafayette, the wind speed was monitored every 8 hours for a one year period. A total of 1095 readings had an average speed of 8.319 mph with a standard deviation of 3.909. An appropriate 1-sided hypothesis test was conducted to test whether the average wind speed at the site is more than 8 mph. Which of the below would be a Type I error for this test?
claim : to test whether the average wind speed at the site is more than 8 mph.
we have : n =1095
mu= population mean = 8
x bar = sample mean = 8.319
s = standard deviation = 3.909
To test : Ho : mu =8 vs H1 : mu > 8 ( it is right tail test )
Test statistics : Z because sample size is large
Z = (x bar - mu ) SQRT(n) / s
Z = 10.555 / 3.909 = 2.700
here we do not have alpha value assume alpha value is 95 %
Z critical value is 1.64 from table
## Decision : we reject Ho if Z statistics value is greater than Z critical value
here Z statistics value is greater than Z critical value .
## Conclusion : our claim is satisfy for alpha value is 95 %
here population mean is greater than 8 here type 1 error is satisfy
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