Question

1. Suppose you collect data on people’s height from a sample of 100 people. The average height in the sample is 66, and the standard deviation of the sample meanis 3 inches.

1. Calculate the 95% confidence interval for the average height in the population
2. At the 12% significance level, test the hypothesis that the average height in the population is 69 inches. Use the four steps we discussed in class.

Calculate the p-value for the hypothesis that the average height in the population is 64 inches.

Answer 1

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 100- 1 ) = 1.984
66 ± t(0.05/2, 100 -1) * 3/√(100)
Lower Limit = 66 - t(0.05/2, 100 -1) 3/√(100)
Lower Limit = 65.4048
Upper Limit = 66 + t(0.05/2, 100 -1) 3/√(100)
Upper Limit = 66.5952
95% Confidence interval is ( 65.4048 , 66.5952 )

To Test :-

H0 :- µ = 69
H1 :- µ ≠ 69

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 66 - 69 ) / ( 3 / √(100) )
t = -10
Test Criteria :-
Reject null hypothesis if | t | > t(α/2, n-1)
Critical value t(α/2, n-1) = t(0.12 /2, 100-1) = 1.568
| t | > t(α/2, n-1) = 10 > 1.568
Result :- Reject null hypothesis

There is not sufficient evidence to support the claim that average height in the population is 69 inches.

To Test :-

H0 :- µ = 64
H1 :- µ ≠ 64

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 66 - 64 ) / ( 3 / √(100) )
t = 6.6667

P - value = P ( t > 6.6667 ) = 0