Ten healthy adult subjects were asked to walk on a treadmill

Ten healthy adult subjects were asked to walk on a treadmill while connected to monitors. One of two kinds of disturbances was applied during the walk, and the number of steps until adaptation was recorded. Each subject experienced both kinds of disturbance, in random order. Here are the summary data for these 10 subjects: The null and alternative hypotheses to test whether there is significant evidence of a different mean adaptation time (in steps) for the two disturbances are: H0: muA = 7.32 and muB = 5.17 vs. HA: muA 7.32 and muA 5.17 H0: muA = muB vs.H0: muA muB H0: mu = 0 vs. H : mu 0 H0: muA = muB vs. H0: muA > muB The test statistic for the appropriate lot of hypothesis is z = 253. t = 2.42. t = 253. z = 2.42. The experimenter stated that the assumptions for the appropriate lot are satisfied. Based on these data, we would reject H0 at significance level 0.10, but not at 0.05. we would reject H0 at significance level 005, but not at 0.02. we would reject H0 at significance level 0.02, but not at 0.01. we would reject H0 at significance level 0.01.

Solution

a)

OPTION C: Ho: u(difference) = 0 vs Ha: u(difference) =/= 0. [ANSWER]

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b)

We use t as we have a small sample, n = 10.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   0  
Ha:    u   =/   0  
              
As we can see, this is a    two   tailed test.      
              
df = n - 1 =    9          
              
Getting the test statistic, as              
              
X = sample mean =    2.15          
uo = hypothesized mean =    0          
n = sample size =    10          
s = standard deviation =    2.68711          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.5301893 = 2.53 [ANSWER, C]          

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c)
              
Also, the p value is              
              
p =    0.032225361          

Thus,

OPTION B: We would reject Ho at significance level 0.05, but not at 0.02. [ANSWER, B]