Question

The Los Angeles County Metropolitan Transportation Authority has set a bus mechanical reliability goal of 3,013 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 64 buses resulted in a sample mean of 3,295 bus miles and a sample standard deviation of 825 bus miles. Is there evidence that the population mean bus miles is greater than 3,013 bus miles? Use α=0.05 level of significance.

1. What is the test statistic? Round answer to 4 decimal places i.e. 0.4582

2.What is the p-value? Round answer to 4 decimal places i.e. 0.4251

3.What is the critical value? Round answer to 4 decimal places i.e. 1.2568

Answer 1

Answer)

Null hypothesis Ho : u = 3013

Alternate hypothesis Ha : u > 3013

1)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (3295-3013)/(825/√64) = 2.7345

2)

As the population s.d is unknown here and we are given with sample s.d as the best estimate

We will use t distribution to estimate the p-value

Degrees of freedom is = n-1 = 63

For 63 dof and 2.7345 test statistics

P-value from t distribution is 0.0041

C)

For 63 dof and 0.05 alpha

Critical value from t distribution is = 1.6694