What is the hypothesis???

The Hypothesis can be simply defined as a supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation. In other words, A hypothesis is a theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false.

Let’s look at an example. My friend (James) hypothesizes to me that “the flowers I plant on my land will grow faster than flowers on your land”. He planted on my land and his land and waters each plant daily for a 3month (experiment) and proves her hypothesis true!

Here, the statement made by my friend is called Hypothesis.

What is Hypothesis testing??? Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.

In the example above, the experiment performed by James is actually what we called hypothesis testing.

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population, or from a data-generating process. The word “population” will be used for both of these cases.

How Hypothesis Testing Works???

In hypothesis testing, the statistician tests a statistical sample, with the aim to provide evidence to the likelihood of the null hypothesis. The test is carried out by measuring and examining a random sample of the population being analyzed. All analysts usually used a random population sample to test two different hypotheses: a null and an alternative Hypothesis.

What is the null Hypothesis??

A null hypothesis is a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove. It is usually denoted by Ho

In the example above, the null hypothesis would be something like this: There is no statistically significant relationship between the lands I used to plant the flowers and the growth of the flowers.

A researcher is challenged by the null hypothesis and usually wants to disprove it, to demonstrate that there is a significant relationship between the two variables in the hypotheses.

What Is an Alternative Hypothesis?

An alternative hypothesis simply is the inverse, or opposite of the null hypothesis. So, if we continue with the above example, the alternative hypothesis would be that “there is indeed a statistically-significant relationship between what type of land used to plant the flower and its growth. To make it more easily the following shows the two hypotheses. Alternative Hypothesis is usually denoted by Ha

Null: If one plant is planted on my land and another one is planted in James’ land, there will be no difference in growth between the two plants.

Alternative: If one plant is planted on my land and another one is planted in James’ land, the plant on James’ land will grow faster than mine.

Mathematically the same Hypothesis can be written as

Ho: Hj=Hm

Ha: Hj>Hm (where Hj and Hm represent the mean height of James’ land plant and my land plant respectively.

What are the steps to be taken for Hypothesis Testing?

All hypotheses are tested using a four-step process:

1. State the two hypotheses i.e. (Determine H0 and Ha. Remember, they are contradictory)

2. Determine the type of test to use.

3. Calculate the tested statistic z using the formula.

4.  Look up the values of z ( called the critical value) from statistical tables. 

5. draw a conclusion. i.e [Compare the calculated test statistic to the Z critical value determined by the level of significance required by the test and make a decision (cannot reject H0 or cannot accept H0), and write a clear conclusion using English sentences.]

How to write the null and alternative hypothesis

Now let us practice some questions on how to write a Hypothesis:

Example1.

The average life of a car battery of a certain brand is six years. This information is gathered using data obtained from people who have purchased and used this brand of battery over a period of several years. A researcher at the battery company develops a new type of car battery and claims that the average life of this battery is more than six years. To determine whether this claim is right, one would need to do some hypothesis testing.

a) What would be the null hypothesis and the alternative hypothesis for this hypothesis test?

b) Assuming the researcher claimed that the average life is not six years. Write out the null and alternative hypotheses.

Solution

a) Null hypothesis: ‘’The average life of the new car battery is six years.’’

Alternative hypothesis: ‘’The average life of the new car battery is more than six years.’’

Mathematically

H0 : μ = 6years

Ha : μ > 6years

(where μ represent the average life of the new car battery)

b) Null hypothesis: ‘’The average life of the new car battery is six years.’’

Alternative hypothesis: ‘’The average life of the new car battery is not six years.’’

Mathematically

H0 : μ = 6years

Ha: μ ≠ 6years

Example2.

Past research data from a period of over several years states that the average life expectancy of cobra is 85 years. A researcher at a laboratory wishes to test this hypothesis. To that end, they procure a sample of the life spans of several cobras. What are the null hypothesis and the alternative hypothesis that this researcher will establish?

SOLUTION

The null hypothesis for the researcher will state that ‘’The average life expectancy of cobra is exactly equal to 85 years.’’

The Alternative hypothesis will read: ‘’The average life expectancy of cobra is not equal to 85 years.’’

Mathematically

H0 : μ = 85years

Ha: μ ≠ 85years

More Explanation: Here the new researcher only wants to know if the statement proposed is likely to be true. Since the previous research state, It is 85years, then the opposite of that will be ‘it is not 85’.

Assuming in the question above that the researcher believes that it should be more than 85 then it should be the following:

H0 : μ = 85years

Ha : μ > 85years

Exampe3.

A company producing groundnut chips claims that each nylon contains 30 groundnut chips on average but I have a feeling that it is not up to that so what will be my null hypothesis and alternative hypothesis??

SOLUTION

Null hypothesis: ‘’The average number of groundnut chips in a nylon is 30.’’

Alternative hypothesis: ‘’ the average number of groundnut chips in nylon is less than 30.’’ (remember I said not up to )

Mathematically

H0 : μ = 30

Ha : μ < 30

Example4

A particular brand of tires claims that its deluxe tire averages at least 20,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 1,000. A researcher believes this is a lie and conducts a survey.

Solution

The null hypothesis: ‘’The average is at least 20,000.’’ i.e more than or equal to 20,000

alternative hypothesis will read: “it is less than 20,000" ( that is the opposite of at least 20,000 stated)

Mathematically

H0: μ ≥ 20000

Ha : μ <20000

Example5

The farmer claims that the weight of the yam on his farm on average is not less than 0.5 kg. A buyer took a random sample of 80 yams from the farm and observed. After a few observations, the buyer believes it shouldn’t up to 0.5kg. Write out the null and alternative hypothesis of the buyer if he is to carry out a hypothesis test.

Solution

From the question, the null hypothesis is that the mean of the yam is not less than 0.5kg i.e greater than or equal to 0.5kg. While the alternative will be the opposite i.e the mean less than 0.5kg

Mathematically

H0: μ ≥ 0.5kg

Ha: μ<0.5kg

Example6

The mean life of a sample of 400 fluorescent bulbs produced by a company is found to be 1570 hours with a standard deviation of 150hours.write the hypothesis that the mean lifetime of the bulbs produced by the company is 1600hours at a 1% confidence level.

Solution

You should always try to figure out the hypothesis statement from the question when it is given. They are always known by figuring out the population parameters from the question. So, if you read the question well then you will realize that the last statement is the hypothesis statement needed.

Null hypothesis: the mean lifetime of the bulbs produced by the company is 1600hours.

Alternative hypothesis: the mean lifetime of the bulbs produced by the company is not 1600hours

Mathematically

H0: μ = 1600years

Ha: μ ≠ 1600years

Example7

The mean weight of 64 men is 63kg. if the weight for the population on average is not more than 60kg, with a standard deviation of 12kg. After using the sample a researcher thinks the average weight stated is not true. write the null and alternative hypotheses.

Solution

Null hypothesis: average not more than 60kg i.e average is either less than or equal to 60kg but not go beyond 60kg

Alternative hypothesis: average is more than 60kg( this is the opposite)

Mathematically

H0: μ ≤ 60kg

Ha: μ > 60kg

Example8

A researcher examined 200 students on academic performances. He discovered that the average score of the students in major courses is 68 with a variance of 8. It is believed that the average score of these students in major courses is 65. Write the hypothesis for this claim.

Solution

Here the hypothesis statement is gotten from the general score belief which is from the second to the last statement.

Null: the average score of these students general score in major courses is 65

Alternative: the average score of these students in major courses is not 65

Mathematically

H0 : μ = 65

Ha: μ ≠65

Example9

In a simple random sample of 600studens taken from a university, 400 are found to be smokers. In another simple random sample of 900 students from another university who are smokers. Write the null and alternative hypothesis out if you to test if the data indicated that there is a significant difference in the habit of smoking in the two universities.??

Solution

Whenever you were given two samples taken from two different populations what you are bound to ask is either there is a significant difference between them or not. When no significant you are trying to say they are the same. Remember how will define the null hypothesis then you will realize that without significant difference is meant for Nullhypothesis while the opposite is for an alternative.

Note: when there is no significance then they would have the same proportion i.e. each of them will be 0.5

Null: no significant i.e. the proportion is Pa=Pb

an alternative: there is a significant difference i.e. Pa ≠Pb

Mathematically

H0: Pa = Pb           

Ha: Pa≠Pb               

Example10

A study was conducted to compare the sexual behavior of students at the University of Ibadan and the University of Lagos. At the University of Ibadan, 200 students were interviewed and 89 said they use condoms during sexual intercourse out of 250 students in the University of Lagos, 50 used condoms. Is there a difference in the proportion?

Solution

Just like the previous question, You don’t need to stress yourself before writing the hypothesis concerning the proportion when you are only trying to know if there is a significant difference or not.

Null: no significant i.e. the proportion is PL=Pi= 0.5

Alternative: there is a significant difference i.e. PL ≠Pi (where PL and Pi represent the proportion of students that use condoms in the university of Lagos and Ibadanrespectively)

Mathematically

H0: Pa = Pb      

Ha: Pa≠Pb               

Did you understand this ?? Yeah, It is as easy as that.

Summary

In short, your null hypothesis is very easy to write as it will always include equal to or specific value. E.g H0 : μ = 85years, H0 : μ = 35kg. it can be in for any of the three below

Two-tailed test one-tailed test one-tailed test

H0: μ = mean Value H0: μ ≤ mean Value H0: μ ≥ mean Value

Ha: μ ≠ mean Value Ha: μ > mean Value Ha: μ < mean Value

The Alternative Hypothesis can be of any of the three below.

1. Ha: μ ≠ 85years (when we are only testing to say it is not equal i.e 2tails test.)

2. Ha: μ > 85years (when we are testing if it is greater than i.e 1tail test.)

3. Ha: μ > 85years (when we are testing if it is less than i.e 1tail test)

That is how to write the null and alternative hypotheses. In my next articles, I will be teaching you how to calcite the Z statistics. I hope you find this article helpful. consider following me for more updates. you can also comment below or chat me up on09153036869follow me on (https://www.instagram.com/abdullahi_oladejo/) for updates. it is your guy Maxwizard!