Question

1.A large government building has received a telephone call threatening that an explosive device has been placed somewhere in the building. The bomb squad has been called to check out the threat and they have ordered all occupants to leave the building. The bomb squad will check out the building and declare whether or not it is safe to renter. (a) State the null and alternate hypothesis that is facing the bomb squad. (b) state the type-I and type-II error in this situation (c) which error is more serious here and why?  

2. A manufacturer of drinking water filters claims that their cartridge last more than 300 liters before they have to be replaced. A consumer group wants to confirm this claim and selects a random sample of 60 cartridges for testing. The cartridges produce a sample average lifetime of 312 liters, and a sample standard deviation of 50 liters. Construct a null and alternate hypothesis that the consumer group should use to confirm the manufacturer’s claim. Based on the sample data, what can the group conclude? Use a 5% level of significance. Would your answer change if you used a 1% level of significance? Justify

Answer 1

1.The null and alternative hypothesis that is faced by bomb squad is as follows :

a)

H_o : bomb is found and building is declared unsafe to enter

H₁ : no bomb is found and building is declared safe to enter

b) type I error : we reject H₀ (null hypothesis ) while it is true.

i.e, bomb squad finds no bomb and declare building safe to enter when bomb is present in the building.

type II error : we accept H₀ while H₁ (alternative hypothesis) is true.

i.e, bomb squads finds a bomb and declares building unsafe to enter while there is no bomb present in the building.

c) looking at the situation it is clear that type I error is more serious as while there is bomb in the building the bomb squad declares it safe to enter again this could lead to explosion with loss of life and lot of damage if it is more . while type II error is less severe in this case because at the least there will be no loss of life and damage to the buliding.