Conduct a hypothesis test to see if the data provide evidence that mean body mas

Question

Conduct a hypothesis test to see if the data provide evidence that mean body mass gain is higher for mice with a light on at night. Show all details of the test.

This includes

1. Hypothesis statements

2. Alpha level you are testing at

3. The statistic you calculate

4. The p-value you get

5. The formal decision

6. The conclusion in context.

The following is the summary table:

Summary Statistics Statistics Sample Size Mean Standard Deviation Minimum Light Dark Overall 9 17 1.010 5.926 8.618 2.624 1.899 3.444 2.79 4.50 6.33 9.05 9.39 9.89 11.20 7.40 17.4 2.79 6.34 9.05 9.89 17.4 Median Q3 Maximum 8.17

Explanation / Answer

H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 > 2 0 i.e. (1 2)

            

Assuming population variances are equal, we would have to calculate pooled-variance t-Test keeping Light SD as S1 and Dark SD as S2

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (9-1)*2.624^2+(8-1)*1.899^2/8+7

         = 80.326415/15

         = 5.355

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(11.01-5.926)-0/5.355(1/9+1/8)

       =4.52

tCRIT is + 1.75305036 at 0.05 and hence reject the null hypothesis because tSTAT>tCRIT.

Conclusion: There is evidence that mean body mass gain is higher for mice with a light on at night.

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