One Tail And Two Tail Tests

3169 words - 13 pages

5a) One and Two Tailed Tests

Suppose we have a null hypothesis H0 and an alternative hypothesis H1. We consider the distribution given by the null hypothesis and perform a test to determine whether or not the null hypothesis should be rejected in favour of the alternative hypothesis.

There are two different types of tests that can be performed. A one-tailed test looks for an increase or decrease in the parameter whereas a two-tailed test looks for any change in the parameter (which can be any change- increase or decrease).

We can perform the test at any level (usually 1%, 5% or 10%). For example, performing the test at a 5% level means that there is a 5% chance of wrongly ...view middle of the document...

We therefore reject the null hypothesis in favour of the alternative at the 5% level.

However, the probability is greater than 0.01, so we would not reject the null hypothesis in favour of the alternative at the 1% level.
Two-Tailed Test

In a two-tailed test, we are looking for either an increase or a decrease. So, for example, H0 might be that the mean is equal to 9 (as before). This time, however, H1 would be that the mean is not equal to 9. In this case, therefore, the critical region has two parts:


Lets test the parameter p of a Binomial distribution at the 10% level.

Suppose a coin is tossed 10 times and we get 7 heads. We want to test whether or not the coin is fair. If the coin is fair, p = 0.5 . Put this as the null hypothesis:

H0: p = 0.5
H1: p ≠ 0.5

Now, because the test is 2-tailed, the critical region has two parts. Half of the critical region is to the right and half is to the left. So the critical region contains both the top 5% of the distribution and the bottom 5% of the distribution (since we are testing at the 10% level).

If H0 is true, X ~ Bin(10, 0.5).

If the null hypothesis is true, what is the probability that X is 7 or above?
P(X ≥ 7) = 1 - P(X < 7) = 1 - P(X ≤ 6) = 1 - 0.8281 = 0.1719

Is this in the critical region? No- because the probability that X is at least 7 is not less than 0.05 (5%), which is what we need it to be.

So there is not significant evidence at the 10% level to reject the null hypothesis.

One-tailed tests

In the previous pages, you learned how to perform define the hypothesis for a statistical test, then to perform a t-test to compare means. In the example t-test we performed, we defined an alternate hypothesis to test whether one mean was greater than the other: μ > μ0.

In this situation, we tested whether one mean was higher than the other. We were not interested in whether the first mean was lower than the other, only if it was higher. So we were only interested in one side of the probability distribution, which is shown in the image below:

In this distribution, the shaded region shows the area represented by the null hypothesis, H0: μ = μ0. This actually implies μ ≤ μ0, since the only unshaded region in the image shows μ > μ0. Because we were only interested in one side of the distribution, or one "tail", this type of test is called a one-sided or a one-tailed test. When you are using tables for probability distributions, you should make sure whether they are for one-tailed or two-tailed tests. Depending on which they are for, you need to know how to switch to the one you need. This is all explained below.

A one-tailed test uses an alternate hypothesis that states either H1: μ > μ0 OR H1: μ < μ0, but not both. If you want to test both, using the alternate hypothesis H1: μ ≠ μ0, then you need to use a two-tailed test.

Two-tailed tests

We would use a two-tailed test to see if two means are different from each other...

Other Essays Like One Tail and Two Tail Tests

Plant Competition Essay

1288 words - 6 pages scale. RESULTS Radish Leaf Length | Radish High | Radish Mixed | Mean | 42.63245 | 31.7856 | Variance | 73.44780158 | 144.792493 | Observations | 22 | 20 | df | 40 | | t Stat | 3.388687743 | | P(T<=t) two-tail | 0.001589122 | | t Critical two-tail | 2.02107539 |   | The significance is to show that this is an example of interspecific competition and which radish is the better competitor. Based on this chart, the

Biol 1003 Antibacterial Action in Garlic

1869 words - 8 pages | | df | 50 | | t Stat | 15.13631 | | P(T<=t) one-tail | 1.32E-20 | | t Critical one-tail | 1.675905 | | P(T<=t) two-tail | 2.64E-20 | | t Critical two-tail | 2.008559 |   | In order for the result to be significant, the P value must be equal to or less than 0.05 The P value of the following graph is 2.87279E-20, which is less than 0.05. The result of Figure 1 is significant. The antibiotic, Ampicillin, has an effect


1331 words - 6 pages higher than 5 times. H0: μ≤5 Ha: μ>5 Formula: t-Test: one sample assuming unequal variance:   | Responses | | Mean | 4.965517 | | Variance | 42.20932 | | Observations | 58 | | Hypothesized Mean | 5 | | df | 57 | | t Stat | -0.04044 | | p-value one tail | 0.5160 | | T critical one tail | 1.672 | | α= 0.05 and df=58-1=57, p-value=0.5160 > 0.05 As t Stat equals to -0.04044, p-value

The RIng Tail Lemur

627 words - 3 pages rosy brown backs with lighter gray or brown hind legs and have white stomachs. The ring-tailed lemur’s length is 37-43 inches. Their weight is 5-8lbs. Their offspring is one. The lifespan of the ring-tailed lemur is 20 years. They have a pointed muzzle, which is typical among the various species of lemurs. Their faces are white and have triangular black noses. Ring-tailed lemurs also have a cute bushy tail.     &nbsp

Business Project

2663 words - 11 pages you get to have one free meal with any one type of wine as you would like to choose. Also we give every customers a gift basket to take home to attract them to come back again. Place: The Yellow Tail is going to be located in Pitt Street, Townhall opposite to the century tower. It has a great location to attract office workers, family and people who like wine. Being in the city the main heart of Sydney it gives us the advantage of stable flow

Evolution of the Alagator

962 words - 4 pages is interesting to note that even though the “super crocs” may have been wiped out, but the smaller version we see today did survive the event. Two other characteristics we see today in alligators are their hard top skin, and long tail. Since the alligator is cold blooded, it uses its skin to help regulate its internal temperature. Since it spends most of its time in the water, the top of the alligator is darker in order to absorb the sunlight

Quality Associates

924 words - 4 pages 3 Standard Deviation = 0.207170594 Sample 4 Standard Deviation = 0.206108999 Yes it appears reasonable since our 4 samples have standard deviations just above .21 in 2 cases and just below .21 in 2 cases. The average standard... Use this for questions 3 & 4 Jean lives about 10 miles from the college where she plans to attend a 10-week summer class. There are two main routes she can take to the school, one through the city and one through the

Experiment 9: Determining Light Preference in Behavioral Ecology of Armadillidium

1237 words - 5 pages , I decided to use statistics to test for the significance of our initial findings. Using the paired t-test function in Excel, p-values were calculated for both a one-tail and a two-tail curve. Using the standard of significance to be .05, we can determine whether our results occurred by chance or because the Pill bugs actually prefer the dark regions. I chose to use the two-tail curve test, because this will provide us with a p-value for

Dalphin Tail

556 words - 3 pages Dolphin Tail. Dir. Charles Martin Smith. Perf. Nathan Gamble, Harry Connick, Jr., Ashley Judd and Morgan Freeman. Warner Brothers. 2011. 1. The protagonist were Sawyer an 11 year old boy who finds a dolphin named Winter on the beach stuck in a crab trap with extensive injuries. Sawyer’s main goal is to save Winter. Another protagonist was Dr. Clay Haskett he is the director of the Clearwater Marine Hospital. The hospital does not have enough

Quantitative Business

955 words - 4 pages the opening gross values were less than 0.39 and 50% were above 0.39. The opening gross was 3.43, which indicates a right tail. The kurtosis of the opening gross was 13.81, which indicates a leptokurtic distribution. This skew can be seen on the first histogram. The graphs are attached on the excel file as well. The opening gross range was 108.43, from 0.01 to 108.44. The standard deviation of opening gross was 18.87. The Interquartile

Qos Recommendation

675 words - 3 pages -probability 100; By default, if you do not configure any drop profile, tail drop profile is in effect and functions as the primary mechanism for managing congestion. In the default tail drop profile, when the fill level is 0 percent, the drop probability is 0 percent. When the fill level is 100 percent, the drop probability is 100 percent. Note :- The default drop profile associated with the packets whose loss priority is low cannot be modified. You can configure custom drop profile only for those packets whose loss priority is high.

Related Papers

Buddhism And Hinduism (Two Worlds That Collide And Combine Into One)

1911 words - 8 pages essence of the Buddhist community showing a slight difference from Hinduism in which there is more than one God. Buddha sought out human suffering is continuous as humans strive after materialistic things which never last therefore causing sorrow. The Buddha focused primarily on this problem and how to solve it is by gaining knowledge. Buddha’s teachings can be predominantly found within the Four Noble Truths and the Noble Eightfold Path; two key

Consideration For Ethics And Diversity Proposal Choose One Or Two Ethical Considerations And One Or Two Diversity Considerations On A Company You Will Research Or Your Present Place Of Employment....

974 words - 4 pages in an effort to appeal to specific customers, this bias can come off as discriminative and reflect negatively on the company. Two areas in need of consideration are appearance-based discrimination and age-based discrimination. ABC Restaurant & Pub, unlike Hooters or certain other establishments, is not protected with a bona-fide occupational qualification defense (BFOQ). Even though our company has not been presented with a legal issue in

Character Comparisons; Comparing Two Characters, One From Streetcar Named Desire And Another From Death Of A Salesman

1908 words - 8 pages Character comparisons; Comparing two characters, one from Streetcar Named Desire and another from Death of a Salesman Streetcar Named Desire Blanche Du Bois In the Streetcar Named Desire, Blanche Dubois is first introduced having dressed in white and symbolizing chastity and innocence. As sensitive, aristocratic, and refined as it is, the beauty depicts an appearance resembling a moth. Blanche comes from a background that is aristocratic. Her

Section One – Extended Response – “Othello’s Downfall Is Due To A Basic Flaw In His Own Character” Discuss And Refer To Two Critical Interpretations

859 words - 4 pages Section one – extended response – “Othello’s downfall is due to a basic flaw in his own character” discuss and refer to TWO critical interpretations. Although many may be under the imperession that Othello’s downfall in the Shakespearean text ‘Othello’, it is thought that Othello isn’t the only character to blame for this tragedy. In the play Othello, Iago orchestrates Othello's downfall like a skillful playwright. Although flaws in