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A researcher claims that a post-lunch nap decreases the amount of time it takes

ID: 3200757 • Letter: A

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 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 when they did not take a post-lunch nap and when they did take a post-lunch nap. At alpha = 0.01, is there enough evidence to support the researchers claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. H_0: mu_d lessthanorequalto d bar H_a: mu_d > d bar H_0: mu_d lessthanorequalto 0 H_a: mu_d > 0 H_0: mu_d greaterthanorequalto d bar H_a: mu_d

Explanation / Answer

Paired Samples Statistics
Mean   N   Std. Deviation   Std. Error Mean
Pair 1   Sprinttimewhthoutnap   4.0067   9   .05362 .01787
Sprinttimewithnap   3.9100   9   .06083 .02028

Paired Samples Test
  
  
Mean   Std. D Std. Error Mean t df   Sig. (2-tailed)
Pair 1   Sprinttimewhthoutnap - Sprinttimewithnap   .09667   .04272   .01424 6.788   8   .000

Null Hypothesis H0:Option E correct

Alternative Hypothesis Ha: Option E correct(Two tailed test)

test statistic t = d bar/SE(d bar) follwos n-1 degree of freedom

where Calculate the difference (di = yi xi) between the two observations on each pair, making sure you distinguish between positive and negative differences.

Calculate the mean difference, d bar

Calculate the standard deviation of the differences, sd, and use this to calculate the standard error of the mean difference, SE( ¯d) = sd / Sqrt(n). = 0.04272

therefore t = 6.788

from t tables the critical value of t at 0.01 level of significance with n-1 = 9 d.fis 3.25

therefore calculated value > table value (6.678>3.25)

therefore H0 is rejected i.e we may conclude that the given data is enough to spport the researchers claim

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