sample1_1 - Sample problems for midterm 1 There will be 4...

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Sample problems for midterm 1 There will be 4 problems on the test similar (and possibly a bit easier, but definitely not harder) to the problems below. 1. An automotive company needs an adhesive with a bond strength in excess of 3500 N/cm 2 . A test of 20 samples of adhesive produced by a potential supplier gave a sample mean of 3650 N/cm 2 and a sample standard deviation of 280 N/cm 2 . Will this result satisfy the auto- motive company if they are looking for strong evidence? Formulate the relevant hypothesis and test at α = 0 . 05. Using the t-table, bound the corresponding P-value. Solution. They would like to be able to show conclusively that μ > 3500. Therefore, the hypothesis that they need to test is H 0 : μ = 3500 versus H 1 : μ > 3500. The relevant test statistic is t 0 = ¯ x - μ 0 s/ n = 3650 - 3500 280 / 20 = 2 . 40 . The corresponding critical value is t 0 . 05 , 19 = 1 . 73, and, since t 0 > t 0 . 05 , 19 , one can reject H 0 which amounts to existence of strong evidence in favor of the bond strength exceeding 3500 N/cm 2 . Using the t-table, we see that t 0 . 025 , 19 < t 0 < t 0 . 01 , 19 . This implies that for the P-value we have 0 . 01 < P < 0 . 025. 2. The probability theorist believes that the temperature of his tea ( T ) is distributed uniformly between 60 and 70 degrees. Let f ( t ) denote the corresponding pdf, and F ( t ) be the cdf. Find the following quantities.
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