Question

to i 26 C 5 C 176 CFal to reject Ho and conclude there is to ect Mg and conclude there is no evidence that耘26 i*less than ps.

Answer 1

Data:      

n1 = 6     

n2 = 6     

x1-bar = 154.8333333     

x2-bar = 396.5     

s1 = 15.93005545     

s2 = 18.52295873     

Hypotheses:      

Ho: μ1 ≥ μ2      

Ha: μ1 < μ2      

Decision Rule:      

α = 0.05     

Degrees of freedom =   6 + 6 - 2 = 10   

Critical t- score =   -1.812461102    

Reject Ho if t <   -1.812461102    

Test Statistic:      

Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] =      √(((6 - 1) * 15.9300554508347^2 + (6 - 1) * 18.5229587269421^2) / (6 + 6 - 2)) = 17.27522311

SE = s * √{(1 /n1) + (1 /n2)} = 17.2752231051681 * √((1/6) + (1/6)) = 9.97385471    

t = (x1-bar -x2-bar)/SE = (154.833333333333 - 396.5)/9.97385471007965 = -24.23001675    

p- value = 1.63272E-10     

Decision (in terms of the hypotheses):      

Since -24.23001675 < -1.812461102 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that the mean blood pressure is significantly higher at 5 ° C than at 26 ° C

ANSWERS:

(a) t = -24.23

Rejection region t ≤ -1.8125

p- value = 0

Option (d)

(b)

Assumptions: Samples are drawn randomly from the populations The two samples are independent Each population is at least 10 times larger than its respective sample. Each sample is drawn from a normal or near-normal population (Skews are less for both samples).

(c)       

n1 = 6

n2 = 6

x1-bar = 154.83

x2-bar = 396.5

s1 = 15.93

s2 = 18.523

% = 95

Degrees of freedom = n1 + n2 - 2 = 6 + 6 -2 = 10

Pooled s = √(((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/DOF) = √(((6 - 1) * 15.93^2 + ( 6 - 1) * 18.523^2)/(6 + 6 -2)) = 17.27521967

SE = Pooled s * √((1/n1) + (1/n2)) = 17.2752196657524 * √((1/6) + (1/6)) = 9.973852724

t- score = 2.228138842

Width of the confidence interval = t * SE = 2.22813884242587 * 9.97385272433209 = 22.22312866

Lower Limit of the confidence interval = (x1-bar - x2-bar) - width = -241.67 - 22.2231286637194 = -263.8931287

Upper Limit of the confidence interval = (x1-bar - x2-bar) + width = -241.67 + 22.2231286637194 = -219.4468713

The 95% confidence interval is [-263.89, -219.45]