Statistics Assignment

Problem 1:

A dairy company bought a machine to pack its 500g packs of butter. The company has doubts that the machine is not accurate. A random sample of 25 packs of butter was chosen and weighted. The average weight of the sample is 507 g and the standard deviation is s=17.5. Does the company have enough evidence to prove that the machine is not accurate in producing 500g packs of butter? (At the α=0.01 level of significance)

Problem 2:

The average monthly rent for a one-bedroom home in San Francisco is $1229 with a standard deviation of $250. A random sample of 15 one-bedroom homes about 20 miles outside of San Francisco had a mean rent of $1350. At α= 0.10, can we conclude that the monthly rent outside San Francisco differs from that in the city?

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