Which type of transformation is shown in the graph?

translation
reflection
rotation
dilatation

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, Null Hypothesis, :  {mean voltage for these two types of

                                                         batteries is same}

Alternate Hypothesis, : {mean voltage for these two types of

                                                            batteries is different]

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

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.

Therefore, we conclude that mean voltage for these two types of batteries is different.