Question

The Statistical Abstract of the United States (109th edition) reported that the mean age of all U.S. registered merchant vessels is 23.6 years. Records for 38 randomly selected U.S. registered grain cargo ships showed that the mean age was 26.7 years with a standard deviation of 5.2 years. Is this type of ship older than the national average of all merchant vessels

Answer 1

Yes, we can conclude that the ship is older than the national average

Explanation:

Population mean, μ = 23.6

Sample mean, xbar = 26.7

Sample size, n = 38

H0 : μ = 23.6

H0 : μ > 23.6

The test statistic :

(xbar - μ) ÷ (σ/√(n))

(26.7 - 23.6) ÷ (5.2/√(38))

3.1 / 0.8435513

Test statistic = 3.675

Decision region :

Reject H0 ; if |Tstatistic| > |Tcritical|

Since we are given the sample standard deviation ; we use the T test distribution

df = 38 - 1 = 37

Tcritical at df = 37 ; α = 0.05 ; rigth tailed :

Tcritical(0.05, 37) = 1.687

3.675 > 1.687 ; Hence, we reject H0 and conclude that there is enough evidence that this type of shop is older than the national average.