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 20 rolls yielded the data provided below, in degrees. at the 1% 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 45°? (note: the sample mean is 46.91° and the sample standard deviation is 11.544°. preliminary data analyses indicate that the distribution is normal.)
a. set up the hypotheses for a one mean test.
( h_0: mu )
( h_1: mu )
(type integers or decimals. do not round.)
b. the test statistic is
(type an integer or a decimal. round to two decimal places as needed.)
c. the p - value is (show your p - value with the rest of your work. you cannot enter it here.
d. the null hypothesis. the data sufficient evidence to conclude that the average angle between the alligators body and its head is the hypothesized mean.

Explanation:

Step1: Set up hypotheses

The null hypothesis \(H_0\) is \(\mu = 45\) (no difference from hypothesized mean). The alternative hypothesis \(H_1\) is \(\mu>45\) (mean is greater than hypothesized).

Step2: Calculate test - statistic

The formula for the \(t\) - statistic in a one - sample \(t\) - test is \(t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}\).
Given \(\bar{x} = 46.91\), \(\mu_0 = 45\), \(s = 11.544\), \(n = 20\).

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Step3: Determine degrees of freedom

Degrees of freedom \(df=n - 1=20 - 1 = 19\)

Step4: Find p - value

Using a \(t\) - distribution table or calculator, for \(t = 0.74\) and \(df=19\) (one - tailed test), \(p - value>0.10\)

Step5: Make a decision

Since \(p - value>0.01\) (significance level \(\alpha = 0.01\)), we fail to reject the null hypothesis.

Answer:

a. \(H_0:\mu = 45\), \(H_1:\mu>45\)
b. \(0.74\)
d. Fail to reject; do not provide; not greater than