Question

A safety officer wants to prove that the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Assume that the speeds of cars are normally distributed.

Provide the notation for the underlined value. That is, what does the underlined value represent?

Answer 1

Answer)

Null hypothesis Ho : u = 25

Alternate hypothesis Ha : u < 25

As the population standard deviation is unknown here and we are using sample s.d as the best estimate

We will use t distribution table to conduct the test

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

t = (24 - 25)/(2.2/√14)

t = -1.7

Degrees of freedom is = n-1 = 13

For 13 dof and -1.7 test statistics

P-value from t distribution is = 0.056458

As the obtained p-value is greater than 0.05

We fail to reject the null hypothesis Ho