Question

The heights of people in the United States is normally distributed with mean 67 inches and standard deviation σ=3.75 inches. We want to know if Lee students are shorter on average than the U.S. population. Use α=0.05.

1. Record the heights (in inches) of all the students in the class.

2. State the null and alternate hypotheses.
   
3. Compute the relevant test statistic.

4. Compute the P-value.

5. State your conclusion using complete sentences.

Data:

72

67

76

62

66

70

66

73

67

66

74

75

67

71

65

60

70

Answer 1

µ = 67, σ=3.75, α=0.05

Mean of sample, x = 68.65

Sample size: n = 17

H0: µ = 67, Lee students are of the same average height as US population

H1: µ < 67, Lee students are shorter on average than the US population

Test statistic: Z = (x-µ)/(σ/n^0.5) = (68.65-67)/(3.75/17^0.5) = 1.81

p-value (Using Excel function NORM.S.DIST(z, cumultaive)) = NORM.S.DIST(1.81,TRUE) = 0.97

Since p-value is more than 0.05, we reject the null hypothesis and conclude that µ < 67, Lee students are shorter on average than the US population.