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.
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 = 0.068 \\)
(round to three decimal places as needed.)
(c) decide whether to reject or fail to reject the null hypothesis.
fail to reject \\( h _ { 0 } \\) because the p - value is greater than \\( \alpha \\).
(d) interpret the decision in the context of the original claim.
there enough evidence at the % level of significance to the claim that the mean dive duration of a north atlantic right whale is minutes.
(type integers or decimals. do not round.)

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value\gt\alpha\), we fail to reject the null hypothesis \(H_0\). If \(P - value\leq\alpha\), we reject the null hypothesis \(H_0\). Here, \(\alpha = 0.01\) and \(P=0.068\).

Step2: Compare the P - value and \(\alpha\)

Since \(0.068>0.01\) (i.e., \(P - value>\alpha\)), we fail to reject the null hypothesis.

Step3: Interpret the result in the context of the original claim

The null hypothesis \(H_0:\mu = 11.6\) (the oceanographer's claim). Failing to reject \(H_0\) means that there is not enough evidence to reject the claim.

Answer:

There is not enough evidence at the \(1\%\) level of significance to reject the claim that the mean dive duration of a North Atlantic right whale is \(11.6\) minutes.