For example, assume an investor wishes to test whether the average daily return of a stock is greater than 1%. A simple random sample of 50 returns is calculated and has an average of 2%. Assume the standard deviation of the returns is %. Therefore, the null hypothesis is when the average, or mean, is equal to 3%. Conversely, the alternative hypothesis is whether the mean return is greater than 3%. Assume an alpha of % is selected with a two-tailed test. Consequently, there is % of the samples in each tail, and the alpha has a critical value of or -. If the value of z is greater than or less than -, the null hypothesis is rejected.

In mathematical statistics , a random variable * X* is standardized by subtracting its expected value
E
[
X
]
{\displaystyle \operatorname {E} [X]}
and dividing the difference by its standard deviation
σ
(
X
)
=
Var
(
X
)
:
{\displaystyle \sigma (X)={\sqrt {\operatorname {Var} (X)}}:}

Beside the professional statistical software Online statistical computation , and the use of a scientific calculator is required for the course. A Scientific Calculator is the one, which has capability to give you, say, the result of square root of 5. Any calculator that goes beyond the 4 operations is fine for this course. These calculators allow you to perform simple calculations you need in this course, for example, enabling you to take square root, to raise e to the power of say, . and so on. These types of calculators are called general Scientific Calculators. There are also more specific and advanced calculators for mathematical computations in other areas such as Finance, Accounting, and even Statistics. The last one, for example, computes mean, variance, skewness, and kurtosis of a sample by simply entering all data one-by-one and then pressing any of the mean, variance, skewness, and kurtosis keys.

Hello Charles,

Thank you very much for your reply!

1) For experiment 1, both data sets that failed the normality test (p= and p=) are not symmetric, according to the box plot. Therefore, a nonparametric test should be used for the analysis, right?

2) For experiment 2, there are two experimental groups. I only have three values for each group. The data for group A are: , , (normality test P<). The data for group B are: , , (normality test P=). The results from t-test (p=) and Mann-Whitney Rank sum test (p=) are very different.

Thank you!

Other factors can be added to this type of test and get more complicated
but most statistical software programs can run Two-Way and Three-Way
ANOVA. Use Two-Way ANOVA when there are two factors.

Two-Way Hypothesis Tests:

Null Hypothesis: There is no difference in the means of the 1st factor

Null Hypothesis: There is no difference in means of the 2nd factor

Null Hypothesis: There is no interaction between the two factors

Alternate Hypothesis: Means are not equal among the levels of the 1st factor

Alternate Hypothesis: Means are not equal among the levels of the 2nd factor

Alternate Hypothesis: There is an interaction between the two factors

When there are 3 or more factors use ANOVA General Linear Model.

Hello Charles,

Thank you very much for your reply!

1) For experiment 1, both data sets that failed the normality test (p= and p=) are not symmetric, according to the box plot. Therefore, a nonparametric test should be used for the analysis, right?

2) For experiment 2, there are two experimental groups. I only have three values for each group. The data for group A are: , , (normality test P<). The data for group B are: , , (normality test P=). The results from t-test (p=) and Mann-Whitney Rank sum test (p=) are very different.

Thank you!