STATISTICAL TECHNIQUES AND TOOLS
TESTS OF SIGNIFICANCE
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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A researcher wishes to determine if people are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose previous research has established that the mean time needed for people to complete a certain maze (without music) is 40 seconds. The researcher, therefore, decides to test the hypotheses H0:µ = 40 versus Ha:µ < 40, where µ is the time in seconds needed to complete the maze while listening to classical music. To do so, the researcher has 10, 000 people complete the maze with classical music playing. The mean time for these people is x-bar = 39.92 seconds, and the P-value of his significance test is 0.0002. Which statement below best describes the appropriate conclusion to draw from this study?
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The researcher has proved that listening to classical music substantially improves the time it takes to complete the maze.
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The researcher has strong evidence that listening to classical music substantially improves the time it takes to complete the maze.
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The researcher has moderate evidence that listening to classical music substantially improves the time it takes to complete the maze.
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Although the researcher has obtained a statistically significant result, it appears to have little practical significance.
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Since the P-value is greater than the reciprocal of the sample size, this is not a significant result.
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Explanation:
Detailed explanation-1: -For performing a t test, we don’t need to know the population standard deviation. The same is true for z test, providing we have a large sample size (>30). Thus the correct option, the condition that is not required is: (b) The population standard deviation a is known.
Detailed explanation-2: -The decision rule refers to the procedure followed by analysts and researchers when deciding whether to reject or not to reject a null hypothesis. We use the phrase “not to reject” because it is considered statistically incorrect to “accept” a null hypothesis.
There is 1 question to complete.