Use the following information to answer Questions 42 44 Ten

Use the following information to answer Questions 42 – 44.

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:

                             N     Mean      StDev    SE Mean

          Disturbance A     10    7.320    2.10016    0.66413  

          Disturbance B     10    5.170    1.86073    0.58842

          Difference A–B    10    2.150    2.68711    0.84974

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:

a)H₀ : m_A = 7.32 and m_B = 5.17 vs. H_a : m_A 7.32 and m_B 5.17

b)H₀ : m_A = m_B vs. H_a : m_A m_B

c)H₀ : m_{Difference A-B} = 0 vs. H_a : m_{Difference A-B} 0

d) H₀ : m_A = m_B vs. H_a : m_A > m_B

The test statistic for the appropriate test of hypothesis is

a) z = 2.53.

b) t = 2.42.

c) t = 2.53.

d) z = 2.42.

The experimenter stated that the assumptions for the appropriate test are satisfied. Based on these data,

a) we would reject H₀ at significance level 0.10, but not at 0.05.

b) we would reject H₀ at significance level 0.05, but not at 0.02.

c) we would reject H₀ at significance level 0.02, but not at 0.01.

d) we would reject H₀ at significance level 0.01.

Solution

1.

b)H0 : mA = mB vs. Ha : mA mB [ANSWER]

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2. As n = 10, we use t.

If ud = the difference in means,

Formulating the null and alternative hypotheses,              
              
Ho:   ud   =   0  
Ha:    ud   =/   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 [ANSWER, C]

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d)          
              
Also, the p value is              
              
p =    0.032225361          

Thus,

OPTION B: we would reject H0 at significance level 0.05, but not at 0.02. [ANSWER]