Math Solutions

(See Steps) A researcher claims that a​ post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of

Question: A researcher claims that a​ post-lunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time​ (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a​ post-lunch nap and when they did take a​ post-lunch nap. At α = 0.05​, is there enough evidence to support the​ researcher's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below.

Male 1 2 3 4 5 6 7 8 9 10
Sprint time​ (without nap) 4.04 4.03 3.91 4.09 3.96 3.93 4.07 4.04 3.98 3.91
Sprint time​ (with nap) 4.03 4.04 3.88 4.09 3.93 3.91 4.08 4.03 3.97 3.89

  1. Identify the claim and state Upper Ho and Ha.
    What is the​ claim?
    Let μd be the hypothesized mean of the difference in the sprint times​ (without nap−with ​nap). What are H0 and Ha​?
  2. Find the critical​ value(s) and identify the rejection​ region(s).
    ​c) Find the standardized test statistic for the t​-test.
    d) Decide whether to reject or fail to reject the null hypothesis.
    e) Interpret the decision in the context of the original claim.
    Price: $2.99
    Solution: The downloadable solution consists of 2 pages
    Deliverable: Word Document


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