A ceiling fan manufacturer claims that 89% of homes in the South have ceiling fans. A random sample of 100 Southern homes was su
rveyed, and 85 had ceiling fans. Let p hat = the proportion of the sample homes that have ceiling fans. The probability that 85% or fewer homes in the South have ceiling fans is 0.098. Does this result provide convincing evidence against the manufacturer’s claim?
Options:
Yes, it is expected that at least 85 homes have ceiling fans.
Yes, the probability of seeing the sample result is so far from what is expected that the probability of it occurring by chance alone is very unlikely.
No, the difference between the sample result and what is expected is not extreme enough.
No, there is a very small chance of seeing the sample result. It is unlikely to occur by chance alone.
Only three dimensional subspace for R3 is R3 itself. In a 3 d subspace there are 3 basis vectors which are all linearly independent vectors. Dimension of a vector is number of subspace in that vector. Finite set can generate infinite dimension vector space.
