Question

an oceanographer claims that the mean dive duration of a north atlantic right whale is 11.6 minutes. a random sample of 35 dive durations has a mean of 12.3 minutes and a standard deviation of 2.2 minutes. at \\( \alpha = 0.01 \\) is there enough evidence to reject the oceanographers claim? complete parts (a) through (d) below. assume the population is normally distributed.
(a) identify the claim and state \\( h _ { 0 } \\) and \\( h _ { a } \\).
\\( h _ { 0 } : \mu = 11.6 \\)
\\( h _ { a } : \mu \
eq 11.6 \\)
(type integers or decimals. do not round.)
the claim is the null hypothesis.
(b) use technology to find the p - value. find the standardized test statistic, t.
\\( t = 1.88 \\)
(round to two decimal places as needed.)
obtain the p - value.
\\( p = \square \\)
(round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 35\). So \(df=35-1 = 34\)

Step2: Calculate the P - value

Since it is a two - tailed test (\(H_{a}:\mu
eq11.6\)) and \(t = 1.88\), we use the t - distribution.
Using a t - distribution table or technology (e.g., a TI - 84 Plus: tcdf(-E99, - 1.88,34)+tcdf(1.88,E99,34)), we find the P - value.
\(P=2\times(1 - P(T\leq1.88))\) (for \(T\) following a t - distribution with \(df = 34\))
Using technology, \(P\approx0.068\)

Answer:

\(P = 0.068\)