Question

5.) A simple random sample of speeds (miles/hour) measured from southbound traffic on Highway 99 towards Bakersfield on a Monday afternoon at 3:30 pm resulted in the following data: n = 27, s = 6.43 m/hr, x̅ = 59.8 m/hr. Assume a normal distribution. Use a 0.05 significance level to test the claim of the highway engineer that the standard deviation of speeds is equal to 5.0 m/hr.

Test Statistic:

Hypotheses:

Diagram:

Conclusion:

Answer 1

Answer:

Given,

Ho : = 5

Ha : != 5

test statistic = (n - 1)s^2/^2

substitute values

= (27 - 1)*6.43^2 / 5^2

= 42.9987

Critical chi square value = (alpha, df) = 38.88513866

= 38.885

Here we observe that, test statistic > critical value, so we reject Ho.

So there is sufficient evidence to support the claim.