Applied Statistics

T-test is any statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is supported.

[h,p,ci] = ttest(y2,0)% return 1 0.0018 ci =2.6280 7.0863

The probability of rejecting the null hypothesis when it is called

the significance level α , and very common choices are

α = 0.05 and α = 0.01

There are four sampling methods:

► Simple Random (purely random),

► Systematic( every kth member of population),

► Cluster (population divided into groups or clusters)

► Stratified (divided by exclusive groups or strata, sample from each group) samplings.

The Alternative hypothesis (denoted by H1 ) is the statement that must be true if the null hypothesis is false.

Given that the population of men has normally distributed weights, with a mean of 173 lb and a standard deviation of 30 lb, find the probability that

a. if 1 man is randomly selected, his weight is greater than 180 lb.

b. if 36 different men are randomly selected, their mean weight is greater that 180 lb.

Solution: a) z = (x - μ)/ σ = (180-173)/30 = 0.23

For normal distribution P(Z>0.23) = 0.4090

b) σ x̄ = σ/√n = 20/√ 36 = 5

z= (180-173)/5 = 1.40

P(Z>1.4) = 0.0808

For binary search, the array should be arranged in ascending or descending order. In each step, the algorithm compares the search key value with the key value of the middle element of the array. If the keys match, then a matching element has been found and its index, or position, is returned. Otherwise, if the search key is less than the middle element's key, then the algorithm repeats its action on the sub-array to the left of the middle element or, if the search key is greater, on the sub-array to the right.

P(x)= p x q n-x n!/[(n-x)!x!]

where n = number of trials

x = number of successes among n trials

p = probability of success in any one trial

q = 1 -p

A hash table is a data structure used to implement an associative array, a structure that can map keys to values. A hash table uses a hash function to compute an index into an array of buckets or slots, from which the correct value can be found.

The null hypothesis (denote by H0 ) is a statement about the value of

a population parameter (such as mean), and it must contain the condition of equality and must be written with the symbol =, ≤, or ≤.

Modeling the relationship between a scalar variable y and one or more variables denoted X. In linear regression, models of the unknown parameters are estimated from the data using linear functions.

polyfit( x,y2,1) %return 2.1667 -1.3333, i.e 2.1667x-1.3333۔

As the sample size increases, the sampling distribution of sample

means approaches a normal distribution

If all possible random samples of size n are selected from a population with mean μ and standard deviation σ, the mean of the sample means is denoted by μ x̄ , so

μ x̄ = μ

the standard deviation of the sample means is:

σ x̄ = σ⁄√ n