An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 37 type K batteries and a sample of 58 type Q batteries. The mean voltage is measured as 8.54 for the type K batteries with a standard deviation of 0.225, and the mean voltage is 8.69 for type Q batteries with a standard deviation of 0.725. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1 be the true mean voltage for type K batteries and μ2 be the true mean voltage for type Q batteries. Use a 0.1 level of significance.

Hypothesis Test states that we will accept 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, = 8.54         and      = 8.69

                 = 0.225       and              =  0.725

                  =  37           and              =  58

                 =  0.585               Here, we use t test statistics because we know nothing about population standard deviations.

     Test statistics =   follows

                             = -1.219

At 0.1 or 10% level of significance t table gives a critical value between (-1.671,-1.658) to (1.671,1.658) at 93 degree of freedom. Since our test statistics is more than the critical table value of t as -1.219 > (-1.671,-1.658) so we have insufficient evidence to reject null hypothesis.

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

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)