Perform the following hypothesis test using the critical value (traditional) met
ID: 3159059 • Letter: P
Question
Perform the following hypothesis test using the critical value (traditional) method. Be sure to state the null and alternative hypotheses, identify the critical value, calculate the test statistic, compare the test statistic to the critical value, and state the conclusion.
A scientist wants to compare the average weights of blue crabs in two river basins, (1) and (2). Based on the health of the two rivers, he believes that the crabs in (2) will be larger, on average, and would like to test for this effect. He randomly samples 100 blue crabs in each basin. The mean weight of the crabs in (1) is 700 grams with a standard deviation of 300 grams. The mean weight of the crabs in (2) is 800 grams with a standard deviation of 400 grams Use = .01 and assume that population variances are not equal.
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u1 - u2 >= 0
Ha: u1 - u2 < 0
At level of significance = 0.01
As we can see, this is a left tailed test.
Calculating the means of each group,
X1 = 700
X2 = 800
Calculating the standard deviations of each group,
s1 = 300
s2 = 400
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 100
n2 = sample size of group 2 = 100
Also, sD = 50
Thus, the z statistic will be
z = [X1 - X2 - uD]/sD = -2
where uD = hypothesized difference = 0
Now, the critical value for z is
zcrit = -2.33
As z > -2.33, WE FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that the crabs in basin 2 are larger on the average than those from basin 1. [CONCLUSION]
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