Question

Alligators perform a spinning​ maneuver, referred to as a​ "death roll," to subdue their prey. In a study of alligator death​ rolls, one of the variables measured was the degree of the angle between the body and head of the alligator while performing the roll. A sample of 2020 rolls yielded the data provided​ below, in degrees. At the 55​% significance​ level, do the data provide sufficient evidence to conclude​ that, on​ average, the angle between the body and head of an alligator during a death roll is greater than 48°​? ​(Note: x bar =44.355 and s equals=10.42°) Preliminary data analyses indicate that you can reasonably use a​ t-test to conduct the hypothesis​ test.

Set up the hypotheses for the​ one-mean t-test.

H0​:μ =

Ha​:μ =

The test statistic is t=

Identify the critical​ value(s). Select the correct choice below and fill in the answer box within your choice.

​(Type an integer or a decimal. Round to three decimal places as​ needed.)

A.The critical value is value is tα = ____

OR

B.The critical values are values are ±tα/2 = ± ____

OR

C.The critical value is value is  −tα = ____

Is the null hypothesis correct?

Answer 1

Solution :

This is the greater tailed test .

The null and alternative hypothesis is ,

H₀ :   = 48

H_a : > 48

Test statistic = t

= ( - ) / s / n

= (44.355 - 48) / 10.42 / 20

= -1.564

= 0.55

df = n - 1 = 19

t _0.55,19 = -0.127

A.The critical value is value is tα = -0.127