Question

Ships arriving in U.S. ports are inspected by Customs officials for contaminated cargo. Assume, for a certain port, 20% of the ships arriving in the previous year contained cargo that was contaminated. A random selection of 50 ships in the current year included 5 that had contaminated cargo. Does the data suggest that the proportion of ships arriving in the port with contaminated cargoes has decreased in the current year? Use α=.01.

Answer 1

Answer :- Ships arriving in U.S. ports are inspected by Customs officials for contaminated cargo. Assume, for a certain port, 20% of the ships arriving in the previous year contained cargo that was contaminated. A random selection of 50 ships in the current year included 5 that had contaminated cargo.

Given that :-

• Sample Size (n) = 50

• X = 5

• Proportion (P) = 20℅ = [ 0.2 ]

• Null Hypothesis and Alternative Hypothesis are :-

=> Null Hypothesis : Ho = 0.2

=> Alternative Hypothesis : HA = P < 0.2

• Sample Proportion :- P^ = X/n

=> P^ = 5/50

=> [ P^ = 0.1 ]

• Test -Statistic :- Z = (P^ - P)/√P(1-P)/n

= (0.1 - 0.2)/√0.2(1-0.2)/50

= -0.1/√0.2(0.8)/50

= -01/√0.16/50

= -0.1/0.0 566

= -1.77

= Test-Statistic => [ Z = -1.77 ]

• P-VALUE :-

=> Significance level = (α = 0.01)

=> P-VALUE = P(z < -1.77)

(using Z table)

=> [ P-VALUE = 0.0384 ]

=> Here, P-value > α

[ P-value(0.0384) > α(0.01) ]

• We fail to reject Null Hypothesis Ho.

Conclusion :- There is no enough evidence to support the claim that the proportion of ships arriving in the port with the contaminated cargo has decreased in the current year.

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