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Using a 0.05 significance level, you need to test the claim that children and adults have...

Using a 0.05 significance level, you need to test the claim that children and adults have the same mean heart rate. Assume that the heart rates of children and adults have equal variances.  What is the value of the test statistic?

Children (age 6-15)

71

83

74

98

115

63

Adults (age > 18)

106

47

90

84

60

77

89
math   Statistics-And-Probability   
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Answer #1

First enter Data into EXCEL

We have to find the sample mean.

Excel command is =AVERAGE(Select data)

sample mean for children = 84

sample mean for Adults = 79

Now we have to find sample standard deviation.

Excel command is =STDEV(Select data)

standard deviation for children = 19.329

standard deviation for Adults = 19.849

n1 = 6

n 2=7

ar{x} = 84

ar{x2} =79

s1 = 19.329

s2 = 19.849

Null and alternative hypothesis is

H0 :u1 = u2

Vs

H1 :u1≠ u2

Level of significance = 0.05

Conclusion: Population variances are equal.

So we have to use pooled variance.

Test statistic is

t=rac{ar{x1}-ar{x2}}{Sp*sqrt{rac{1}{n1}+rac{1}{n2}}}

nln2-2

(6- 1)373.610(7 1)393.983 6+7-2

Sp=V 1868.05+ 2363.98

Sp= 19.61

84-79 = 1961 *

19.61 0.5563

t- 10.909

t 0.458

t=0.46

The value of the test statistic is t=0.46

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