In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation 37,500 miles. Calculate the appropriate test statistic to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

The test statistics is  

Step-by-step explanation:

From the question we are told that

    The  sample size is  n =  191 \  buses

     The sample mean is  

    The population standard deviation is  

The null hypothesis is  

The alternative hypothesis is  

Generally the test statistics is mathematically represented as

=>      

=>      

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).