Experienced academic writing professionals are at your fingertips.
Use this handy tool to get a price estimate for your project.

Step 4: We compare the *p*-value to alpha, which we will let alpha be 0.05. Since 0.0044 is less than 0.05 we will reject the null hypothesis and decide in favor of the alternative, *H*_{a}.

Before actually conducting a hypothesis test, you have to put two possible hypotheses on the table — the null hypothesis is one of them. But, if the null hypothesis is rejected (that is, there was sufficient evidence against it), what’s your alternative going to be? Actually, three possibilities exist for the second (or alternative) hypothesis, denoted H_{a}. Here they are, along with their shorthand notations in the context of the pie example:

When you set up a hypothesis test to determine the validity of a statistical claim, you need to define both a null hypothesis and an alternative hypothesis.

Note: In computing the Z-test statistic for a proportion we use the hypothesized value *p _{o}* here not the sample proportion p-hat in calculating the standard error! We do this because we "believe" the null hypothesis to be true until evidence says otherwise.

Every hypothesis test contains a set of two opposing statements, or hypotheses, about a population parameter. The first hypothesis is called the denoted H_{0}. The null hypothesis always states that the population parameter is to the claimed value. For example, if the claim is that the average time to make a name-brand ready-mix pie is five minutes, the statistical shorthand notation for the null hypothesis in this case would be as follows:

The "Z-value" (-2.62) is the test statistic. It is a standardized score for the difference between the sample p and the null hypothesis value p = .40. The *p-*value* is* the probability that the z-score would lean toward the alternative hypothesis as much as it does if the true population really was p = .40.

Versatile Services that Make Studying Easy

We write effective, thought-provoking essays from scratch

We create erudite academic research papers

We champion seasoned experts for dissertations

We make it our business to construct successful business papers

What if the quality isn’t so great?

Our writers are sourced from experts, and complete an
obstacle course of testing to join our brigade. Ours
is a top service in the English-speaking world.

How do I know the professor
won’t find out?

Everything is confidential. So you know your student
paper is wholly yours, we use CopyScape and WriteCheck
to guarantee originality (never TurnItIn, which
professors patrol).

What if it doesn’t meet my expectations?

Unchanged instructions afford you 10 days to
request edits after our agreed due date. With
94% satisfaction, we work until your hair is
comfortably cool.

Clients enjoy the breezy experience of working with us

Click to learn our proven method

The "*Z*-value" (-2.62) is the test statistic. It is a standardized score for the difference between the sample p and the null hypothesis value p = .40. The *p-*value* is* the probability that the z-score would lean toward the alternative hypothesis as much as it does if the true population really was p = .40.

A small *p*-value favors the alternative hypothesis. A small *p*-value means the observed data would not be very likely to occur if we believe the null hypothesis is true. So we believe in our data and disbelieve the null hypothesis. An easy (hopefully!)way to grasp this is to consider the situation where a professor states that you are just a 70% student. You doubt this statement and want to show that you are better that a 70% student. If you took a random sample of 10 of your previous exams and calculated the mean percentage of these 10 tests, which mean wouldbe **less likely** to occur if in fact you were a 70% student (the null hypothesis): a sample mean of 72% or one of 90%? Obviously the 90% would be less likely and therefore would have a small probability (i.e. p-value).

How do you know which hypothesis to put in H_{0} and which one to put in H_{a}? Typically, the null hypothesis says that nothing new is happening; the previous result is the same now as it was before, or the groups have the same average (their difference is equal to zero). In general, you assume that people’s claims are true until proven otherwise. So the question becomes: Can you prove otherwise? In other words, can you show sufficient evidence to reject H_{0}?

**NOTATION**: The notation *H*_{o} represents a null hypothesis and *H*_{a} represents an alternative hypothesis and p_{o} is read as p-not or p-zero and represents the null hypothesized value. Shortly, we will substitute μ_{o} for when discussing a test of means.

Generally, this failure to see that one could name numerical variables is sort of an interesting case of the language or notation one uses preventing a certain kind of thinking. That's something that's certainly discussed in ordinary linguistics. In its popular versions, it's often called the Sapir-Whorf hypothesis.

89%

of clients claim significantly improved grades thanks to our work.

98%

of students agree they have more time for other things thanks to us.

Clients Speak

“I didn’t expect I’d be thanking you for actually
improving my own writing, but I am. You’re like a second professor!”