"A study is performed in San Antonio to determine whether the average weekly grocery bill per five-person family in the town is significantly different from the national average, which is $131. A random sample of 50 five-person families in San Antonio showed a mean of $133.474 and a standard deviation of $11.193." Assume that the national average weekly grocery bill for a five-person family is $131. Is the sample evidence statistically significant? If so, at what significance levels can you reject the null hypothesis?

Prove the divisibility of the following numbers: ! i have no any is 1. 16^5 + 2^15 by 33 2. 15^7 + 5^13 by 30

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

1. if events a and b are non-overlapping events, how do you find the probability that one or the other occurs? 2. what does it mean if p(a or b) equals 1?