A researcher teaches rats to recognize a specific object that by giving them their favorite treat when they touched the object. To measure their ability to recognize the specific object a week later, she records the number of times the rat touches the specific object compared to a different object. It was hypothesized that the rats would touch the specific object more than the different object to demonstrate what they learned about the specific object. If the researcher tested this hypothesis at a .05 level of significance and computes a test statistic of t = 2.842 in a sample of 28 rats, what is the degree of freedom for the test?

The degree of freedom for the test is 27.

Step-by-step explanation:

The experiment performed by the researcher is to determine the number of time the rat touches the specific object compared to a different object.

The parameter under study is the mean number of times the rat touches the specific object.

The hypothesis for the test is defined as:

H₀: The mean number of times the rat touches the specific object is not more than that for a different object, i.e. μ ≤ μ₀.

Hₐ: The mean number of times the rat touches the specific object is more than that for a different object, i.e. μ > μ₀.

A t-test for single mean is performed.

The information provided is:

α = 0.05

t = 2.842

n = 28

The degrees of freedom for a single mean t-test is:

df = (n - 1)

   = 28 - 1

   = 27

Thus, the degree of freedom for the test is 27.

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

each side has a different length.  

step-by-step explanation: