Question

A university claims its recent graduates earn an average annual salary of

$45,000. You draw a random sample of 40 recent graduates and find that their
average salary is $46,000, and calculate the standard error of the sample mean
as 436.81. What is the t ratio for this result?

Answer 1

t-ratio = 0.362

Explanation:

In hypothesis testing,

The t-ratio is given by the formula:

`(X-\mu)/(s)`

where μ is the hypothesized mean, X the sample mean and s the sample standard deviation

The Standard Error of the Mean SEM =
`\large \text{{$(s)/(√(n))$}}` where n is the sample size.

We We are given:

X = 46,000
μ= 45,000

SEM = 436.81

n = 40

We can find the sample standard deviation
s = SEM x √n
s = 436.81 x √ 40

s = 2762.3

Therefore

t-ratio = (46000 - 45000)/2762.3 = 0.362