The world’s smallest mammal is the bumblebee bat. Such bats are roughly the same
ID: 3316366 • Letter: T
Question
The world’s smallest mammal is the bumblebee bat. Such bats are roughly the same size of a large bumblebee. Listed below are the weights (in grams) from a sample of these bats. Assuming that all such bats have a standard deviation of .3 grams, use a significance level of .05 to test the claim that these bats are from the same population with a known mean of 1.8 grams. Do the bats appear to be from the same population ? You may assume the sample data comes from a population that follows a normal distribution. 2.13 1.31 1.91 1.92 1.77 1.64 2.29 1.99 2.33 2.49 2.22
1. State the null hypothesis H0: _____________
2. State the alternative hypothesis H1: _____________
3. What is the test statistic used for the test (z or t)
4. State the significance or alpha () level
5. Determine the p-value.
6. Do you or do you not reject the null hypothesis? Why?
7. Write a clear conclusion using a complete sentence.
Explanation / Answer
H observed: mu is equal to 1.8 grams
H alternate: mu is not equal to 1.8 grams
t = (x - mu) / (S / radical n)
= (sample mean - population mean) / (standard deviation / the square root of the number of samples)
The mean and standard deviation of the sample data are: x = 2 and S = 0.3423.
t = (2 - 1.8) / (0.3423 / radical 11) = 2.211
The t value can be calculated with a TI-84 by going to STAT, TESTS, T-Test.
After entering data (numbers should be Stats, 1.8, 2, .3423, 11, and the "not equal" sign), hit Calculate.
You will see the t value, 1.938, and p value, .0814.
If you cannot perform this test, the p value can be calculated this way:
Go to 2nd VARS, tcdf( -enter the lower bound (the t value), the upper bound (we usually use 1000, and the df (degrees of freedom).
The df = n - 1 = 11 - 1 = 10
The display should look like this: tcdf(1.938,1000,10) ENTER.
The value should be .0407. Since this is a two-tailed test, meaning the "not equal sign" was used instead of "less than" or "greater than" when stating the hypotheses, the p value must be multiplied by two. Now, the correct p value should be .0814.
We are asked to use a significance level (a) of .05.
Is the p value less than or equal to a?
Is .0814 less than or equal to .05?
No- now we must state the conclusion in context:
Since the p value of .0814 is greater than a, which equals .05, we can fail to reject the null (observed) hypothesis. There is sufficient evidence to conclude that the sample bats are from the same population.
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