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

Answer 1

The value of the np is 10, and the value of the nq is 40 which is less than 5 also the hypothesis H0: p = 0.20 versus H1: p<0.20

What are the null hypothesis and alternative hypothesis?

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

We have:

n = 50

p = 20% = 0.02

q = 1-p = 1- 0.02 = 0.08

$\rm n_p = 50 \times 0.20 = 10\\\\\rm n_q = 50\times 0.80 = 40$

$\rm n_q > 5\\\\\rm n_p > 5$

The conditions are verified for this test.

Null hypothesis H0: The number of ships arriving in ports with hazardous cargoes has remained constant.

Alternative hypothesis H1:  The number of ships arriving in port with polluted goods has dropped.

H0: p = 0.20 versus H1: p<0.20

Thus, the value of the np is 10, and the value of the nq is 40 which is less than 5 also the hypothesis H0: p = 0.20 versus H1: p<0.20

Learn more about the null hypothesis and alternative hypothesis here:

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