Question

You are currently working at NCLEX Memorial Hospital in the Infectious Diseases Unit. Over the past few days, you have noticed an increase in patients admitted with a particular infectious disease. You believe that the ages of these patients play a critical role in the method used to treat the patients. You decide to speak to your manager, and together you work to use statistical analysis to look more closely at the ages of these patients.

The data set consists of 65 patients that have the infectious disease with ages ranging from 41 years of age to 84 years of age for NCLEX Memorial Hospital.

Age

69

41

57

55

45

59

71

71

72

67

60

65

73

72

42

45

65

47

44

51

71

66

84

56

61

59

68

73

50

55

77

57

47

71

58

49

65

60

44

61

57

63

61

60

62

55

66

50

77

66

66

65

57

69

59

70

53

76

74

68

55

61

81

43

67

Continue the hypothesis test based on the claim that the average age of all patients admitted to the hospital with infectious diseases is less than 64 years of age.

Show your results and formulas used for the following calculations:

• Test Statistic
• Critical Value
• P-value

How is this done in EXCEL??

Answer 1

Solve using Excel functions:

Mean: x = AVERAGE( ) = 61.292

Standard deviation: s = STDEV.S( ) = 10.218

n = 65, μ = 64

Degrees of freedom: df = n-1 = 65-1 = 64

Level of significance = 0.05

H₀: μ = 64

H₁: μ < 64

Test statistic: t = (x-μ)/(s/n^0.5) = (61.292-64)/(10.218/65^0.5) = -2.137

Critical value (Using Excel function T.INV(probbability, df)) = T.INV(0.05,64) = -1.669

p-value (Using Excel function T.DIST(test statistic, df, cumulative)) = T.DIST(-2.137, 64, TRUE) = 0.018

Since p-value is less than 0.05, we reject the null hypothesis and conclude that μ < 64.

So, average age of all patients admitted to the hospital with infectious diseases is less than 64 years.