Thursday, September 29, 2016

For the hypothesis test, we need to find the test statistics
t = (x-bar - Mu)/standard error
standard error = sample standard deviation/square root of n
From here we compare the test statistic to the critical value t or you can compute the p-value and compare to alpha level of the test at .05
If the p-value < alpha, then reject Ho. Notice in the case of your problem, there is a rejection of the null hypothesis in both cases.
For the confidence interval it's mean +/- tcritical*standard error.

Friday, September 23, 2016

To calculate the Q1 (25th percentile) take n times .25 and that value is the data value that is Q1. If n(.25) does not come out even, round up to the next integer. Remember the data values must be sorted in order from lowest to highest for this. Q3 is found by taking n(.75) and round up if necessary and that is the value in order of Q3, IQR is interquartile range and is Q3-Q1. We use that to find out if there are any outliers. Any data value less than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR) is an outlie

Wednesday, September 14, 2016

Mean (x + y) = Expected value (X + Y) = E(x) + E(y) which means the mean is meanx + meany, so is meanx = 75 and meany =70, then the mean (x +y) =  75 + 70 = 145
The Var(x + y) = Var(x) + Var(y) if x and y are independent.
Var(x) = 6^2 = 36
Var(y) = 8^2 + 64
Var(x+y) = 100. The standard deviation is the square root of the variance, so standard deviation = 10
The mean of the difference is the difference of the means E(X - Y) = mean (x - y) = meanx - meany
So the difference of the means is 75-70 = 5
The standard deviation of the difference is the square root of the Var(x-y)
Var(x - y) = Var(x) + Var(y) if x and y are independent, same as for Var(x +y) . Therefore the answer is 10