##P(O,O) = 2/12 xx 1/11 = 1/66## For probability questions, think of each event happening separately, it makes the maths easier to understand. For example, in this question, do not think of the two boys taking a fruit at the same time – that makes the maths complicated . Let Daniel take a fruit first, then Sean can take a fruit. There are two parts to consider. ##Probability = “number of desirable outcomes”/”total number of possible outcomes”## For Daniel: there are 12 different pieces of fruit in the bowl, he just takes one without choosing a specific fruit. (random) The […]

Using a z-score table: The area of the tails must be .05 (which is 1 – .95), and each tail must be .05/2, or .025. Find .025 in the interior part of a z-score table. See that it corresponds to a z-score (the numbers in the margins) of 1.96. That is the answer. Using a TI-83 or TI-84 graphing calculator: 2nd VARS > invNorm(.025,0,1) gives you -1.96, which is -z. So, z = 1.96.

See the explanation below. The answer is with particular reference to the Normal distribution. A test procedure starts with fixing the level of significance at 5% or 10% or 1% and so on. When we say that level of significance is 5%, we admit that our results are likely to be erroneous in 5% cases. That is why a test procedure with 5% level of significance reflects a 95% confidence interval. From the area table of a standard normal curve, we find that Pr [##mu## – ##sigma## < x < ##mu## + ##sigma##} is about .30 Pr[##mu## – 2##sigma## < […]

Measures of center are a way to try capture the non-randomness of a population or a random variable.This may sound a bit confusing,so I will walk through the 3 most common measures of center and explain how they try to do that. Mean . The mean is the most common measure of center and it tries to capture what is , in average, the process value .It poses the simple question: If I kept repeating this process , sum all the outcomes and divide by the number of trial, what value should I expect? The mean shines in practical use […]

I have found a nice example for you to check out on the Penn State web page. With the final notice saying: “Comparing two proportions – For proportions there consideration to using “pooled” or “unpooled” is based on the hypothesis: if testing “no difference” between the two proportions then we will pool the variance, however, if testing for a specific difference (e.g. the difference between two proportions is 0.1, 0.02, etc — i.e. the value in Ho is a number other than 0) then unpooled will be used.” as a quick sum up. here is a link to a detailed […]