Answer:
1. Null Hypothesis, :
{mean voltage for these two types of
batteries is same}
Alternate Hypothesis, :
{mean voltage for these two types of
batteries is different]
2. Test Statistics value = -5.06
4. Decision for the hypothesis test is that we will reject null hypothesis.
Step-by-step explanation:
We are given that an engineer is comparing voltages for two types of batteries (K and Q).
where, = true mean voltage for type K batteries.
= true mean voltage for type Q batteries.
So, <em>Null Hypothesis, </em><em> : </em>
<em> {mean voltage for these two types of </em>
<em> batteries is same}</em>
<em>Alternate Hypothesis, </em><em> : </em>
<em> {mean voltage for these two types of </em>
<em> batteries is different]</em>
The test statistics we use here will be :
follows
where, = 9.29 and
= 9.65
= 0.374 and
= 0.518
= 83 and
= 77
=
= 0.45 Here, we use t test statistics because we know nothing about population standard deviations.
Test statistics = follows
= -5.06
<em>At 0.05 or 5% level of significance t table gives a critical value between (-1.98,-1.96) to (1.98,1.96) at 158 degree of freedom. Since our test statistics is less than the critical table value of t as -5.06 < (-1.98,-1.96) so we have sufficient evidence to reject null hypothesis.</em>
Therefore, we conclude that mean voltage for these two types of batteries is different.