Question

CHALLENGE ACTIVITY 5.7.1: Hypothesis test for the difference between two population means. > Jump to level 1 The mean voltage and standard deviation of 5 batteries from each manufacturer were measured. The results are summarized in the following table. Manufacturer Sample mean voltage (millivolts) Sample standard deviatio A 167 B 164 3 What type of hypothesis test should be performed? Select What is the test statistic? Ex: 0.123 What is the number of degrees of freedom? Ex 250 Does sufficient evidence exist to support the claim that the voltage of the batteries made by the two manufacturers is different at the a = 0.01 significance level? Select 2 Check Next

Answer 1

a) As we are testing here whether the voltage of the batteries made by the two manufacturers is different, therefore this is a case of a two tailed difference in means test here. This is a case of a t test of difference between the means here.

b) The standard error here is computed as:

12 + 32 SE = + - 1.4142 ni n2 5

Therefore the test statistic here is computed as:

$t^* = \frac{\bar X_1 - \bar X_2}{SE} = \frac{167 - 164}{1.4142} = 2.121$

Therefore 2.121 is the test statistic value here.

c) the degrees of freedom here is computed as:
Df = n₁ + n₂ - 2 = 8

Therefore 8 is the degrees of freedom here.

d) As this is a two tailed test, the p-value here is obtained from t distribution tables as:
p = 2P( t₈ > 2.121) = 2*0.0333 = 0.0666

As the p-value here is 0.0666 > 0.01, which is the level of significance here, therefore the test is not significant here and therefore we cannot reject the null hypothesis here. Therefore we dont have sufficient here that the voltage of the batteries made by the two manufacturers is different