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27. A manufacturer claims its Brand A battery lasts longer than its competitor's Brand B battery. Nine batteries of
each brand are tested independently, and the hours of battery life are shown in the table below.
Brand A
Brand B
88
80
85
79
80
77
81
82
72
75
90
81
85
77
85
73
84
78
Provided that the assumptions for inference are met, which of the following tests should be conducted to
determine if Brand A batteries do, in fact, last longer than Brand B batteries?
(A) A one-sided, paired 1-test
(B) A one-sided, two-sample t-test
(C) A two-sided, two-sample t-test
(D) A one-sided, two-sample z-test
(E) A two-sided, two-sample z-test

Sagot :

According to the desired test, the test that should be conducted is:

  • (B) A one-sided, two-sample t-test

Test:

  • At the null hypothesis, it is tested if Brand A batteries do not last longer than Brand B batteries, that is, the result of the subtraction is of at most 0:

[tex]H_0: \mu_A - \mu_B \leq 0[/tex]

  • At the alternative hypothesis, it is tested if it is greater, that is:

[tex]H_1: \mu_A - \mu_B > 0[/tex]

The factors determining the test used are as follows:

  • We can find the standard deviation for the sample, hence a t-test is used.
  • There are two samples, the lifetimes for batteries A and for batteries B, hence, a two-sample test is used.
  • We are testing if one mean is greater than another, and more than/less than tests are one-sided.
  • Hence, option B is correct.

You can learn more about test hypothesis at https://brainly.com/question/13873630

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