STATISTICS 4th QUARTER EXAM
Familiarize the Z table and try to locate the ff critical or tabular value
Level of Significance
1.
2.
3.
4.
5.
6.
Types of Tests
One-tailed
Two-tailed
0.10
+/-1.282
+/-1.645
0.05
+/-1.645
+/-1.960
0.01
+/-2.326
+/-2.576
critical value of z given: two tailed test, δ = 0.10
critical value of z given: one tailed test, δ = 0.05
99% confident and two tailed test
critical value if the researcher is 90% confident and Ha:p<76
critical value if the researcher is 95% and Ha:p=74
critical value if the researcher is 95% confident and Ha:p<54
Use T-table for the ff. problem
1. critical value of t given: one tailed test, δ = 0.01, df = 14
2. critical value of t given: two tailed test, δ = 0.10, df = 14
3. critical value of t given: one tailed test, δ = 0.05, df = 8
To draw conclusions about a population from sample data – Primary purpose of hypothesis
testing
null hypothesis (Ho) - It is the initial claim and assumes no.
Alternative Hypothesis - It is contrary to the null hypothesis and shows there is a significant
relationship or difference.
If the computed value is less than the tabular value – (Left-tail test) Reject the null hypothesis
Failing to reject the null hypothesis when it is true – correct statement
level of significance (α) - It is the degree of uncertainty or doubtfulness
Level of confidence - is the degree of assurance or certainty that a particular statistical statement
is correct under specified conditions.
critical value (cv) or tabular value - separate the area of acceptance and the area of rejection
𝑥̅ −𝜇
𝑧 = 𝜎/ 𝑛, x̄ = sample mean
√
Area of rejection - is the area under the normal curve wherein the null hypothesis is rejected
based on the set condition or Decision Rule.
Area of rejection – also known as critical region
Z – test - a type of test is used if the sample (n) is greater than (>) 30
𝑥̅ −𝜇
𝑧 = 𝜎/ 𝑛 = formula of Z-test of One population mean
√
Accept Ho - If the Computed value is < -cv or > +cv
Reject Ho - If the Computed value is > -cv or < +cv
p = po – not an alternative hypothesis (population proportion)
p ≠ po – two-tailed test
p < po – lower-tailed test
p > po – upper-tailed test
Z-test - test statistics used in Population Proportion
Bivariate - It comes from the word “Bi” meaning two and “Variate” meaning variable
Karl Pearson - First derived a Pearson correlation by a British Statistician named
Pearson (r) - It is a technique that is commonly used in determining the relationship between two
sets of data.
There are 3 types of correlation
1. Perfect positive Correlation
2. Perfect Negative Correlation
3. No Correlation
X - Independent Variable Representation
Y - Dependent Variable Representation
Perfect relationship - Interpretation of Coefficient Correlation if r is equal to 1
Linear Regression- It is a line that shows the relationship between two variables by a linear
equation
Using the Linear Regression Formula:
1. Find the Area of n=61 and e=10%.
2. Find the Area of n=101 and e=25%.