Exam 2 Monday Review Solutions

Exam 2 Monday Review Solutions - h1 Bjork Larsen needed to...

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Stat 350 Exam 2 Monday Review Solutions page 1 of 5 h1 Bjork Larsen needed to determine whether to use a new racing wax for the Swedish Nordic Ski Team. He thinks that the new wax will be worth the price if it would lead to a faster race time, on average. In the past, the average time for a standard length race was 1.40 hours. He selects a random sample of 36 Swedish skiers and has each use the new wax system for the upcoming standard length race. a. Let μ = the average race time for all Swedish skiers using the new wax system. State the appropriate hypotheses to be tested. H 0 :__ μ = 1.4 ___ H a :__ μ < 1.4 ___ Some SPSS output based on the race times for the 36 skiers is provided at the right and below. b. Complete the sentence. The histogram does not look approximately normal, rather, it is somewhat skewed to the __ left ____. However, the t-test result can still be considered valid due to what main result? The CLT or Central Limit Theorem One-Sample Statistics 36 1.330 .124 .021 Race Time (hours) N Mean Std. Deviation Std. Error Mean Race Time (hours) 1.50 1.40 1.30 1.20 1.10 1.00 Frequency 10 9 8 7 6 5 4 3 2 1 0 One-Sample Test 35 .002 -.070 -.112 -.028 Race Time (hours) t df Sig. (2-tailed) Mean Difference Lower Upper 95% Confidence Interval of the Difference Test Value = 1.40 c. What is the distribution of the test statistic if the new wax system does not lead to faster race times on average? Final answer: ___ t(35) distribution ____ d. The value of the test statistic is missing in the SPSS output. Provide its value and the corresponding p -value for testing the hypotheses in part (a). p -value = _ 0.002/2 = 0.001 _____ e. Based on the test results, which of the following is the appropriate real-world conclusion? Clearly circle your answer. i. The new wax system significantly decreased the average race time supporting its use by the Swedish Nordic Ski Team. ii. There was insufficient evidence to demonstrate the new wax system decreased the average race time.
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