s of cans of diet soda have weights with a mean that is less than the mean for the regular soda. hypotheses? B. Ho P1=2
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Data on the weghts of contents of cans of diet soda :
Sample size , n = 40.
Sample mean , x̅ = 0.78473 lb.
Standard deviation , s = 0.00438 lb.
Data on the weghts of contents of cans of regular soda :
Sample size , n = 40
Sample mean , x̅ = 0.81044.
Standard deviation , s =0.00741.
Given level of significance, α = 0.01.
Notice, Here population standard deviations are equal.
When this is the case we use a pooled t-test.
It is asked to find
· The null and alternative hypotheses.
Claim : Mean weghts of contents of cans of diet soda is less than mean weghts of contents of cans of regular soda
Based on the claim the hypotheses being tested is ,
Null hypotheses , Ho : µ1 µ2
Alternative hypotheses , Ha : µ1 < µ2
Since we've less than inequality in alternative hypotheses it is left tailed test.
Thus , the claim is in alternative hypotheses.
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