Excel to Conduct a t-test for Two Samples - Statistics HW Help




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Day

Night

36

16

58

30

64

34

71

37

71

40

74

45

75

56

76

61

76

62

77

68

77

69

78

74

79

79

82

80

85

80

86

80

87

80

87

83

88

84

88

84

93

85

93

87

93

87

94

88

94

88

95

88

95

88

96

90

97

91

97

91

98

91

99

92

100

92

100

94

105

98

100


Day

Night

Mean

84.68571429

Mean

74.77777778

Standard Error

2.385097792

Standard Error

3.569960898

Median

87

Median

83.5

Mode

93

Mode

80

Standard Deviation

14.11042883

Standard Deviation

21.41976539

Sample Variance

199.1042017

Sample Variance

458.8063492

Kurtosis

2.81565835

Kurtosis

0.699234634

Skewness

-1.349649357

Skewness

-1.280291357

Range

69

Range

84

Minimum

36

Minimum

16

Maximum

105

Maximum

100

Sum

2964

Sum

2692

Count

35

Count

36

\[\begin{array}{cc} & {{H}_{0}}:\sigma _{1}^{2}=\sigma _{2}^{2} \\ & {{H}_{A}}:\sigma _{1}^{2} \not = \sigma _{2}^{2} \\ \end{array}\] \[F = \frac{s_{1}^{2}}{s_{2}^{2}}\]

F-Test Two-Sample for Variances

Night

Day

Mean

74.77778

84.68571

Variance

458.8063

199.1042

Observations

36

35

df

35

34

F

2.304353

P(F<=f) one-tail

0.00834

F Critical one-tail

2.249408


\[\begin{array}{cc} & {{H}_{0}}:{{\mu }_{1}}\ge {{\mu }_{2}} \\ & {{H}_{A}}:{{\mu }_{1}}<{{\mu }_{2}} \\ \end{array}\] \[t=\frac{({{{\bar{X}}}_{1}}-{{{\bar{X}}}_{2}})-({{\mu }_{1}}-{{\mu }_{2}})}{\sqrt{\frac{s_{1}^{2}}{{{n}_{1}}}+\frac{s_{2}^{2}}{{{n}_{2}}}}}\]

t-Test: Two-Sample Assuming Unequal Variances

Night

Day

Mean

74.77777778

84.68571429

Variance

458.8063492

199.1042017

Observations

36

35

Hypothesized Mean Difference

0

df

61

t Stat

-2.307711554

P(T<=t) one-tail

0.012211224

t Critical one-tail

1.670218808

P(T<=t) two-tail

0.024422449

t Critical two-tail

1.999624146