The Data in the Excel file Assignment4.xlsx under Q1 are the means of 1000 samples of size 5 "S5" and of size 30 "S30" drawn from an exponential distribution with mean 0.5.

A) Draw a histogram for both cases and comment on the distributions, i.e. is it (approximately) symmetric? Why yes/why not?

B) Find the mean and the standard error of both and compare them to the exact mean and standard error.

S5 S30

.52 .49

.50 .39

.50 .48

.90 .66

.56 .59

.51 .57

.45 .43

.48 .39

.44 .50

.22 .50

.69 .46

.73 .70

.27 .46

.55 .39

.62 .68

.36 .47

.21 .54

.66 .41

.75 .55

.20 .44

.39 .38

.71 .49

.41 .42

.16 .35

.89 .67

.94 .58

.73 .47

.44 .37

.30 .60

.46 .47

.24 .54

.57 .59

.72 .45

.54 .57

.68 .43

.54 .64

.38 .50

.56 .61

.89 .50

.31 .42

.59 .48

.74 .62

.29 .56

.50 .48

.35 .59

.51 .45

.64 .61

.41 .44

.48 .48

.39 .42

.41 .47

.72 .51

1.04 .67

.44 .54

.43 .40

.37 .52

.53 .41

.60 .53

.20 .59

.72 .73

.40 .45

.54 .49

.51 .43

.31 .35

.53 .51

.36 .42

.67 .60

.58 .46

.49 .46

.27 .39

.25 .47

.13 .35

.31 .56

.42 .58

.27 .47

.88 .47

.29 .54

.60 .47

.20 .49

.39 .48

1.22 .54

.39 .45

.31 .42

.08 .44

.85 .59

.53 .44

.20 .58

.91 .35

.76 .57

.50 .52

.91 .65

.48 .50

.50 .39

.18 .46

.60 .48

.36 .42

.52 .46

.54 .51

.48 .58

.45 .42

.28 .47

.31 .59

.24 .55

.41 .40

.37 .40

.97 .48

1.35 .50

.65 .46

.51 .50

.75 .41

.58 .46

.64 .60

.68 .45

.32 .39

.48 .46

.30 .34

.26 .62

.49 .46

.52 .55

.37 .45

.36 .47

.50 .47

.45 .52

.54 .30

.50 .43

.46 .67

1.01 .68

.27 .51

.39 .42

.41 .54

.73 .45

.42 .59

.41 .49

.76 .72

.54 .54

.49 .45

.37 .28

.39 .38

.20 .28

.69 .54

.26 .48

.38 .49

.38 .51

.51 .42

.20 .35

.51 .43

.42 .51

.38 .52

.64 .48

.49 .50

.47 .42

.99 .55

.36 .41

.52 .51

.61 .57

.67 .39

.56 .49

.50 .42

.30 .27

.48 .47

.61 .48

.45 .57

.40 .39

.27 .36

.13 .38

.64 .61

.35 .46

.75 .58

.60 .55

.38 .46

.29 .52

.25 .35

.35 .50

1.09 .55

.85 .46

.47 .60

.32 .48

.31 .42

.48 .61

.54 .54

.30 .40

.79 .72

.92 .44

.41 .40

.38 .52

.40 .32

.64 .49

.43 .33

.62 .57

.68 .44

.30 .55

1.18 .73

.40 .36

.32 .41

.25 .54

.33 .53

.46 .39

.50 .39

.25 .39

.39 .45

.51 .51

.30 .53

.27 .43

.32 .52

.54 .57

.56 .53

.52 .48

1.03 .58

.39 .56

.17 .39

.50 .56

.27 .56

.34 .47

.63 .46

.56 .60

.64 .51

.79 .41

1.06 .66

.33 .43

.58 .60

.51 .44

.24 .48

.14 .45

.48 .48

.53 .50

.45 .76

.26 .33

.23 .42

.51 .43

.82 .52

.48 .55

.59 .51

.72 .47

.46 .35

.09 .39

.35 .55

.49 .43

.34 .38

.66 .44

.44 .50

.14 .40

.31 .48

.21 .41

.09 .52

.15 .35

.94 .61

.91 .67

.62 .45

.26 .52

.69 .72

.33 .38

.29 .35

.51 .52

.54 .51

.16 .39

.30 .48

.64 .64

.56 .37

.47 .62

.39 .48

.15 .50

.20 .38

.71 .48

.34 .47

.58 .58

.38 .43

.81 .66

.58 .44

.81 .37

.33 .55

.22 .60

.62 .49

.32 .44

.21 .37

.73 .47

.45 .52

.57 .40

.55 .48

.17 .46

.20 .52

.41 .40

.38 .48

.32 .47

.44 .56

.23 .34

.53 .48

.78 .53

.24 .33

.40 .48

.31 .44

.47 .43

.25 .45

.30 .49

.84 .57

.31 .46

.95 .57

.78 .56

.54 .38

.34 .41

.85 .49

.53 .54

.61 .56

.30 .44

.46 .42

.36 .49

.15 .43

.52 .51

.44 .43

.32 .58

.97 .68

.43 .52

.44 .49

.35 .54

.25 .34

.34 .52

.74 .39

.28 .38

.67 .34

.28 .48

.30 .47

.35 .55

.57 .57

.26 .38

.39 .51

.28 .36

.60 .62

.26 .54

1.02 .62

.38 .50

.30 .57

.83 .54

.61 .75

.67 .55

.77 .64

.69 .61

.94 .60

.49 .54

.63 .50

.66 .54

.39 .44

.52 .53

.51 .55

.32 .47

.35 .64

.97 .56

.45 .87

.36 .63

.56 .65

.42 .57

.51 .46

.58 .64

.21 .41

.31 .47

.28 .50

.44 .48

.62 .45

.42 .43

.54 .49

.47 .53

.63 .40

.81 .55

.64 .49

.44 .45

.20 .39

.54 .47

.28 .32

.95 .63

1.37 .62

.62 .51

.31 .55

.41 .44

.42 .65

.47 .58

.99 .51

.55 .39

.55 .60

.45 .41

.22 .48

.59 .56

.63 .56

.29 .49

.50 .41

.48 .46

.39 .47

.44 .34

.62 .51

.54 .62

.22 .68

.26 .49

1.05 .48

.40 .39

.58 .49

.87 .52

.94 .60

.82 .39

.63 .50

.23 .44

.30 .36

.77 .67

.14 .43

.47 .53

.34 .53

.74 .61

.66 .56

.79 .42

.41 .43

.55 .49

1.26 .53

1.27 .63

.59 .38

.46 .37

.56 .42

.19 .51

.13 .45

.60 .58

.45 .61

.64 .51

.54 .54

.44 .38

.65 .54

.14 .57

.71 .47

.31 .71

.45 .59

.37 .51

.49 .62

.76 .56

.27 .42

.34 .45

.64 .50

.26 .37

.24 .49

.97 .54

.26 .45

.57 .64

.29 .43

.67 .48

.43 .39

.47 .51

.52 .53

.16 .45

.48 .35

.64 .45

.47 .28

.50 .51

.36 .40

.57 .55

.53 .52

.46 .48

.65 .60

.63 .40

.52 .59

.41 .50

.27 .38

.75 .58

.35 .59

.24 .42

.73 .56

.56 .38

.39 .40

.78 .66

.29 .43

.66 .43

.17 .41

.60 .43

.50 .65

.82 .55

.65 .57

.58 .42

.53 .54

.24 .36

.83 .48

.57 .57

.47 .53

.42 .46

.47 .52

.44 .38

.59 .52

.34 .41

.37 .38

.78 .59

.37 .60

.40 .45

.59 .48

.35 .60

.37 .47

.32 .47

.67 .69

.48 .55

.34 .50

.41 .64

.41 .56

.67 .62

.16 .37

.40 .44

.28 .59

.23 .45

.58 .40

.45 .46

.63 .52

.70 .51

.54 .43

.56 .62

.51 .45

.28 .50

.50 .57

.57 .49

.52 .49

.69 .49

1.25 .62

.80 .66

.17 .30

.37 .52

.61 .56

.98 .48

.62 .76

.43 .47

.15 .34

.41 .36

.16 .43

.50 .59

.65 .49

1.02 .52

.45 .61

.41 .47

.64 .52

.14 .44

.43 .36

.93 .76

.37 .59

.45 .55

.73 .57

.31 .47

.35 .46

.21 .41

.53 .59

.44 .46

.53 .51

.35 .53

.31 .53

.42 .49

.43 .47

1.13 .67

.27 .51

.83 .66

.68 .53

.39 .37

.53 .59

.21 .39

.71 .57

.30 .37

.53 .45

.93 .54

.55 .40

.45 .33

.42 .30

.59 .54

.52 .64

.43 .43

.82 .50

.71 .70

.46 .46

.55 .45

.45 .56

.36 .40

.35 .61

.35 .33

.69 .63

.32 .49

.94 .48

.23 .56

.72 .52

.34 .47

.30 .49

.19 .42

.39 .46

.20 .43

.52 .47

.50 .39

.27 .32

.33 .51

.38 .28

.47 .45

.67 .48

1.00 .65

.65 .57

.47 .60

.57 .53

.44 .56

.49 .55

.62 .41

.63 .51

.65 .31

.45 .42

.79 .58

.14 .66

.81 .46

.67 .49

.98 .48

.67 .52

.72 .45

.38 .45

.38 .58

.41 .49

.47 .56

1.18 .48

.40 .54

.31 .57

.25 .40

.26 .50

.14 .50

.26 .52

.29 .52

.36 .51

.41 .46

.61 .58

.73 .59

.24 .48

.32 .40

.64 .52

.31 .45

.53 .40

.95 .50

.50 .39

.25 .50

.40 .35

.80 .55

.55 .44

.66 .62

.75 .38

.56 .60

.59 .49

.67 .47

.42 .66

.21 .57

.51 .53

.26 .46

.69 .55

.65 .60

.49 .53

.98 .46

.90 .48

.39 .57

.88 .50

.65 .56

.40 .54

.59 .44

.22 .43

1.12 .57

.24 .42

.34 .36

.63 .55

.86 .53

.37 .36

.41 .46

.26 .59

.26 .55

.58 .54

.87 .50

.24 .52

.55 .63

.62 .46

.32 .60

.40 .45

.45 .47

.42 .57

.65 .45

.37 .56

.39 .42

.56 .53

.24 .47

.16 .46

.37 .46

.38 .60

.56 .52

.67 .44

.77 .54

.33 .49

1.26 .72

.73 .75

.17 .40

.35 .59

.33 .43

.54 .46

.62 .62

1.27 .58

.48 .50

.38 .50

.50 .45

.42 .47

.65 .39

.70 .52

1.03 .67

.29 .62

.77 .52

.68 .53

.42 .54

.27 .28

.86 .66

.52 .54

.22 .57

.43 .46

1.38 .68

.68 .51

.96 .57

.41 .45

.25 .44

.31 .48

.53 .54

.59 .48

.23 .58

.35 .35

.46 .51

.44 .43

.55 .44

.32 .42

.54 .52

.20 .45

.49 .40

.70 .47

.58 .87

.20 .36

.34 .55

.42 .41

.74 .42

1.08 .58

.50 .54

.71 .73

.56 .48

1.04 .52

.22 .65

.22 .41

.35 .45

.41 .47

.90 .56

.41 .43

.42 .45

.52 .63

.42 .49

.25 .68

.45 .40

1.27 .56

.33 .53

.32 .41

.57 .46

.22 .31

.59 .56

.37 .53

.52 .66

.20 .55

.25 .49

.71 .54

.58 .47

.25 .38

.65 .60

.78 .60

.97 .65

.30 .51

.56 .58

.62 .80

.41 .48

.21 .53

.47 .62

.99 .71

.63 .51

.33 .57

.22 .29

.39 .51

.33 .62

.52 .46

.44 .49

1.10 .53

.81 .56

.60 .57

.26 .55

.57 .47

.51 .59

.77 .54

.46 .46

.34 .32

.46 .42

1.13 .55

.29 .51

.58 .36

.29 .45

.84 .69

1.11 .65

.37 .47

.63 .66

.48 .55

.53 .46

.40 .40

.23 .45

.53 .51

.67 .51

.62 .49

.75 .57

.73 .66

.23 .42

.47 .43

.70 .69

.18 .52

.19 .43

.40 .67

.75 .50

.70 .57

.74 .44

.56 .55

.41 .53

.32 .55

.40 .58

.29 .51

.35 .45

.23 .30

.20 .44

.42 .37

.50 .42

.73 .53

.45 .59

.78 .59

.68 .44

.22 .48

.45 .40

.93 .58

.80 .63

.54 .51

.80 .44

.95 .47

.27 .43

.35 .35

.30 .42

.20 .45

.30 .38

1.06 .65

.30 .42

.35 .62

.34 .41

.51 .67

.39 .42

.51 .51

.55 .52

.66 .42

1.06 .56

.54 .45

.60 .44

.93 .69

.46 .40

.27 .34

.21 .32

.62 .48

.48 .61

.58 .47

1.03 .66

.41 .37

.91 .62

.49 .55

.52 .43

.39 .59

.36 .55

.52 .47

.16 .23

1.08 .55

1.16 .64

.46 .38

.48 .32

.42 .50

.44 .63

.23 .51

.36 .59

.56 .63

.57 .59

.62 .48

.89 .52

.66 .52

.36 .46

.65 .53

.38 .39

.79 .83

.46 .62

.48 .40

.47 .59

.54 .55

.40 .38

.25 .49

.38 .57

.43 .45

.38 .48

.32 .34

.35 .48

.27 .45

.54 .45

.31 .55

.63 .44

.57 .39

.48 .46

.16 .45

.72 .60

.10 .39

.45 .51

.39 .37

.71 .58

.30 .44

.56 .46

.36 .41

.42 .41

.39 .37

.43 .58

.64 .37

.63 .45

.32 .55

.33 .38

.63 .55

.75 .75

.30 .59

.40 .44

.26 .43

.52 .44

.32 .50

.18 .50

.52 .38

.36 .61

.51 .59

.78 .45

.53 .48

.33 .52

.69 .53

.66 .48

.49 .49

.46 .48

.51 .40

.89 .50

.60 .46

.25 .51

.76 .55

.58 .43

.65 .35

.44 .51

.27 .38

.79 .47

.40 .53

.22 .32

.15 .39

.89 .67

.53 .41

.76 .64

.62 .55

.15 .42

.61 .48

.42 .46

.57 .36

.44 .50

.31 .46

.50 .52

.53 .55

.39 .39

.29 .53

.40 .53

1.00 .61

.23 .34

.93 .82

.24 .40

.26 .37

.74 .53

.36 .37

.49 .44

.60 .43

.43 .42

.28 .33

.30 .46

.39 .41

.50 .43

.58 .50

.40 .46

.46 .54

.55 .41

.24 .60

.52 .75

.20 .56

.55 .35

.29 .33

.41 .45

.88 .61

.45 .52

.34 .56

.53 .59

.87 .53

.66 .60

.26 .34

.32 .45

.31 .45

.34 .52

.69 .57

.27 .53

.11 .59

.52 .42

.51 .63

.45 .48

.42 .52

.31 .33

.49 .44