Hypothesis Testing Flashcards
Hypothesis testing or significance testing is a part of
inference statistics
It is a method for testing a claim about a parameter of interest in a population using data measured in a sample
hypothesis testing
is a statement or a tentative theory that may or may not be true but is initially assumed to be true until new evidence suggests otherwise
hypothesis
hypothesis of “no difference” and usually formulated for the purpose of being rejected.
null hypothesis
This is the hypothesis that contradicts the null hypothesis and is also the operational statement of the experimenter’s research hypothesis.
alternative hypothesis
State the null and alternative hypothesis of the following problems
A senior high school teacher of a certain university claimed that the average grade of their senior high school students in General Math subject is at least 85. He randomly selects 40 students and found out an average grade of 84 with a standard deviation of 3.
Claim: The average grade of senior high school students in General Math subject is at least 85. (𝜇≥85)
Counterclaim: The average grade of senior high school students in General Math subject is less than 85. ( 𝜇<85)
State the null and alternative hypothesis of the following problems
A marketing agency claims that a typical person use his facebook account for more than 40 minutes per day, on the average. To test this claim a sample of 35 persons where asked.
Claim: A typical person use his facebook account more than 40 minutes per day, on the average. (𝜇>40 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦)
Counterclaim: A typical person use his facebook account at most 40 minutes per day, on the average. (𝜇≤40 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦)
. In order to keep an adult female healthy and hydrated she has to drink an average of 11 cups of water daily as advised by a nutritionist. Is the advised of the nutritionist true?
state the null and alternative hypothesis
Claim: To keep an adult female healthy and hydrated she has to drink an average of 11 cups of water daily (𝜇=11 𝑐𝑢𝑝𝑠 𝑑𝑎𝑖𝑙𝑦)
Counterclaim: To keep an adult female healthy and hydrated she doesn’t have to drink an average of 11 cups of water daily
(𝜇≠11 𝑐𝑢𝑝𝑠 𝑑𝑎𝑖𝑙𝑦)
a procedure, based on sample evidence and probability theory, used to determine whether the hypothesis is a reasonable statement and should not be rejected, or is unreasonable and should be rejected.
hypothesis testing
steps in hypothesis testing (7)
State the null hypothesis (Ho) and alternative hypothesis (Ha), decide what data to collect and
under what conditions
2. Specify the level of significance and the sample size n
3. Find the sampling distribution of the test statistics under the assumption that Ho is true
4. Establish the critical region for the test statistics
5. Computation of the test statistics, for a sample size n
6. Make a decision.
7. Create a conclusion.
is the error committed when the null hypothesis is rejected when it is true
type I error
is the error committed when the null hypothesis is accepted when it is false
type II error
When we claim that the batches of cellphone is in good condition, when in fact they are not, then TYPE _ error is committed.
I
If we claim that the batches of cellphone is not in good condition, when in fact they are, then type _ error is committed
type II
denoted by α (alpha)
level of significance
The probability of committing Type II error is denoted by
beta
power of test to denote type II error
(1 - B)
At 0.05 level, the researcher is willing to accept a 5% chance of being wrong decision when Ho is rejected. If Ho is rejected at 0.05 level, then it is usually labeled as
significant
At 0.01 level, the researcher is willing to accept a 1% chance of being wrong when Ho is rejected. If Ho is rejected at 0.01 level, then the result is labeled “
highly significant
In addition, for a fixed sample size n, decreasing one type of error would mean increasing the other type of error and the only way to decrease both type of errors simultaneously is by increasing the ___
sample size
the alternative hypothesis specifies that the unknown population mean is entirely above or entirely below the specified value of the null hypothesis.
directional test or one tailed test
The following are classified as directional or one-tailed test
a. Ho : µ = 100 Ha : µ < 100
b. Ho : µ = 50 Ha : µ > 50 c. Ho : µ = 710 Ha : µ > 710
the alternative hypothesis specifies that the unknown population mean can lie on either side of the value specified by null hypothesis.
non-directional or two-tailed test
The following are classified as non-directional or two-tailed test
a. Ho : µ = 100 Ha : µ ≠ 100
b. Ho : µ = 50 Ha : µ ≠ 50
c. Ho : µ = 710 Ha : µ ≠ 710
State whether the given alternative hypothesis is a directional or a non-directional test.
A senior high school teacher of a certain university claimed that the average grade of their senior high school students in General Math subject is at least 85. He randomly selects 40 students and found out an average grade of 84 with a standard deviation of 3.
Formulated hypotheses: 𝐻𝑜:𝜇≥85 and 𝐻𝑎: 𝜇<85
Since the alternative hypothesis indicates a specific direction, that is less than.
Therefore, it is considered as a directional test.
State whether the given alternative hypothesis is a directional or a non-directional test.
A marketing agency claims that a typical person use his facebook account for more than 40 minutes per day, on the average. To test this claim a sample of 35 persons were asked.
Formulated hypotheses: 𝐻𝑜: 𝜇≤40 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦 and
𝐻𝑎: 𝜇>40 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦
Since the alternative hypothesis indicates a specific direction, that is greater than.
Therefore, it is considered as a directional test.
In order to keep an adult female healthy and hydrated she has to drink an average of 11
cups of water daily as advised by a nutritionist. is the advised of the nutritionist true?
State whether the given alternative hypothesis is a directional or a non-directional test.
Formulated hypotheses: 𝐻𝑜:𝜇=11 𝑐𝑢𝑝𝑠 𝑑𝑎𝑖𝑙𝑦 and 𝐻𝑎: 𝜇≠11 𝑐𝑢𝑝𝑠 𝑑𝑎𝑖𝑙𝑦
Since the alternative hypothesis indicates no specific direction, that is not equal to.
Therefore, it is considered as a non-directional test.
is a value determined from sample information and is used to determine whether or not the null hypothesis will be rejected.
test statistic
some examples of test statistic
𝒛−𝒕𝒆𝒔𝒕, 𝒕−𝒕𝒆𝒔𝒕, 𝑭−𝒕𝒆𝒔𝒕, 𝝌^𝟐 (𝒄𝒉𝒊−𝒔𝒒𝒖𝒂𝒓𝒆 𝒕𝒆𝒔𝒕)
do practice exercises on powerpoint (slides 17)
+1
4.2.1 Test of Hypothesis for the Mean µ with known variance σ2 formula
view reviewer
is symmetric probability distribution centered at zero and looks similar but more variable (spread out) than the normal distribution.
t-distribution
The t-distribution becomes more and more similar with the normal distribution as the ____ increases.
number of freedom
do practice problems on test statistic
+1
is the dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.
critical value
study computations on critical values
+1
is the fraction or percentage that indicates the part of the population or sample having a particular trait of interest.
proportion
The sample proportion is denoted by p and is found by:
𝑝=(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑒𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒)/(𝑛𝑢𝑚𝑏𝑒𝑟 𝑠𝑎𝑚𝑝𝑙𝑒𝑑)
Also called the paired t-test
dependent t-test
It intends to test whether there is a significant difference between the means from the same group.
dependent t-test
Mostly used in comparing pre-test and post-test results
dependent t-test
It is used to test the null hypothesis:
dependent t-test
null hypothesis of dependent t-test
𝜇𝑏𝑒𝑓𝑜𝑟𝑒 = 𝜇𝑎𝑓𝑡𝑒r
dependent t test formula
view reviewer
The samples from each population must be independent of one another.
z-test for independent samples
The populations from which the samples are taken must be normally distributed and the population variances are known,
z-test for independent samples
the sample sizes must be large i.e. n1≥30 and n2≥30.
z-test for independent samplse
Also called the two-sample t-test for independent samples
t-test for independent samples
It intends to test whether there is a significant difference between the means of two unrelated groups
t-test for independent samples
The populations from which the samples are taken must be normally distributed and the population variances are known,
t-test for independent samples
It is used to test the null hypothesis: 𝜇1 = 𝜇2
t-test independent samples
Applicable in comparing more than two independent samples.
analysis of variance
Extension of t-test for independent samples.
analysis of variance
Reject the Ho if Fc>Ftab or p<0.05
analysis of variance
assumption for ANOVA (3)
The population from which the samples were drawn arenormally distributed.
The samples are independent from each other.
The variances of the different samples are homogeneous
decision to reject Ho if p value is what to alpha
p value < alpha
sometimes also referred to as the F-test is applicable in comparing three or more independent sample means
ANOVA (analysis of variance)
null hypothesis for ANOVA
u1 = u2 = u3 …
alternative hypothesis for ANOVA
Ha: at least one mean is different
SSB meanin
sum of square between
meaning of SSW
sum of squares within
meaning of SST
total sum of squares
two component of mean square
MSB
MSW
ratio of mean squares
F-computed (Fc)
