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Answer: The expected value of the water depth is 4.5 m.
Step-by-step explanation:
Let x be a random variable which is uniformly distributed in interval [a,b] .
Then the mean of the distribution is ghiven by :-
Given : While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.
Then, the expected value of the water depth =
Hence, the expected value of the water depth is 4.5 m.
Answer:
The <em>p</em>-value is 0.0802.
Step-by-step explanation:
The hypothesis for a test is defined as:
<em>H₀</em>: <em>μ</em> = 800 vs. <em>Hₐ</em>: <em>μ</em> ≠ 800
A two tailed test for the population mean can be performed using a <em>z</em>-test or a <em>t</em>-test.
A <em>z</em>-test is used if the data provided has information related to the population standard deviation and the sample size is large, i.e. <em>n </em><u>></u> 30.
And if the population standard deviation is not known and the sample size is small, then the <em>t</em>-test will be used.
Since there is no information about either the population standard deviation or the sample size, assume that <em>z</em>-test is used.
The test statistic value is:
<em>z</em> = 1.75
Compute the <em>p</em>-value of the test as follows:
*Use a <em>z</em>-table for the probability.
Thus, the <em>p</em>-value is 0.0802.