Question

A field biologist wants to test whether two species of mice have the same mean mass. She collects two random samples of 10 mice from each species and measures their mass in grams. The results are shown in the following table. Assume that both species have a standard deviation of 6.5 grams and that the mass for each species is normally distributed. Let the number of field mice be the first sample, and let the number of rock mice be the second sample.

She conducts a two-mean hypothesis test at the 0.01 level of significance, to test if there is evidence that both species have the same mass.

For this test: H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.

Field mice	Rock mice
142	139
161	142
162	130
135	129
138	132
148	140
134	154
157	128
145	149
161	124

Use a TI-83, TI-83 Plus, or TI-84 calculator to test if the means are different. Identify the test statistic, z, and p-value from the calculator output. Round your test statistic to two decimal places and your p-value to three decimal places.

Provide your answer below:

test stat = ____ p-valu = ____

Answer 1

Since the standard deviations are known, we are going to use Z test.

Mean (A) of field mice = 148.3

Mean (B) of rock mice = 136.7

Our random variable in this test is (D)= A - B

Now, as the two samples are independent, variance of( D = A - B) = (X2 / n ) + (Y2 /n) where x and y are the known standard deviations.

variance= (6.5*6.5/10) + (6.5*6.5/10) = 16.9

standard deviation (S of D) = 16.9 = 4.11

our test statistic = (148.3 - 136.7)/ (4.11) = 2.82

p-value = 0.005

level of significance is 0.01 and the test is two tailed. So, the critical values will be the points with probabilities 0.005,which are 2.58.

test statistic is > 2.58 and p value < 0.1

therefore we reject null hypothesis.