$2.25 $2.41 $2.30 $2.55 $2.57 $2.65 $2.28 $2.42 $2.32 $2.59 $2.39 $2.64 $2.31 $2

Question

$2.25

$2.41

$2.30

$2.55

$2.57

$2.65

$2.28

$2.42

$2.32

$2.59

$2.39

$2.64

$2.31

$2.43

$2.49

$2.60

$2.34

$2.79

$2.33

$2.45

$2.51

$2.61

$2.38

$2.59

$2.35

$2.47

$2.53

$2.63

$2.67

$2.73

$2.37

$2.48

$2.54

$2.52

$2.58

$2.56

Assume the alpha value is .05.  Find the mean, standard deviation and confidence interval.

$2.25

$2.41

$2.30

$2.55

$2.57

$2.65

$2.28

$2.42

$2.32

$2.59

$2.39

$2.64

$2.31

$2.43

$2.49

$2.60

$2.34

$2.79

$2.33

$2.45

$2.51

$2.61

$2.38

$2.59

$2.35

$2.47

$2.53

$2.63

$2.67

$2.73

$2.37

$2.48

$2.54

$2.52

$2.58

$2.56

Explanation / Answer

mean=sum(x)/n=89.63/36=2.4897

sd=sqrt(sum((x-mean)2)/n)=sqrt(0.6429/36)=0.1336

here sample size n=36 ( more than 30) so we use z-value to find the confidence interval

(1-alpha)*100% confidence interval for population mean=sample mean±z(alpha/2)*sd/sqrt(n)

95% confidence interval for population mean=sample mean±z(0.05/2)*sd/sqrt(n)=

=2.4897±1.96*0.1336/sqrt(36)=2.4897±0.0436=(2.4463, 2.5333)

following information has been generated using ms-excel

n= 36 sample mean= 2.4897 sd= 0.1336 z-value margin of error lower limit upper limit 95% confidence interval 1.96 0.0436 2.4463 2.5333

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