Calculating P-Values for H_0: \mu =\mu_0

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In summary, the conversation discusses calculating the p-value for a test statistic in a hypothesis testing scenario where H_0: \mu =\mu_0 and H_1: \mu \neq\mu_0. The equation used is P=2[1-\Phi(z_0)], with the probability value obtained from a normal distribution table. For part (e), the equation to be used is P=2[1-\Phi(-z)].
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Homework Statement


Suppose that we are testing H_0: [tex]\mu[/tex] =[tex]\mu_0[/tex] versus H_1: [tex]\mu[/tex] [tex]\neq[/tex][tex]\mu_0[/tex]. Calculate the P-value for the following observed values of the test statistic.
a: z_0 =2.45
e: z_0=-0.25


Homework Equations


none


The Attempt at a Solution


I got part a by using the equation, P=2[1-[tex]\Phi[/tex](z_0)]. I got the value for the probability from the table in the book since it's a normal distribution and the p-value was equal to .014286.
Then for part e, I tried using the same equation as before, but I got a p-value of 1.19. My equation was P=2[1-.401294]
Can someone help with what I'm doing wrong? Thanks in advance
 
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  • #2
For part (e), use [itex]\Phi[/itex](-z) = 1 - [itex]\Phi[/itex](z).
 

FAQ: Calculating P-Values for H_0: \mu =\mu_0

What is a p-value?

A p-value is a statistical measure that helps determine the likelihood of obtaining results at least as extreme as the observed data, assuming the null hypothesis is true. It is typically used in hypothesis testing to determine the significance of a relationship or difference between two groups.

How is a p-value calculated?

The p-value is calculated by determining the probability of obtaining the observed data or more extreme data under the assumption that the null hypothesis is true. This is usually done by comparing the observed data to a probability distribution, such as the normal distribution, and finding the area under the curve that represents the observed data.

What does a p-value of less than 0.05 mean?

A p-value of less than 0.05 indicates that there is a less than 5% chance of obtaining the observed data or more extreme data if the null hypothesis is true. In other words, there is strong evidence to reject the null hypothesis and support the alternative hypothesis.

What does a p-value greater than 0.05 mean?

A p-value greater than 0.05 indicates that there is a greater than 5% chance of obtaining the observed data or more extreme data if the null hypothesis is true. This suggests that there is not enough evidence to reject the null hypothesis and the results are not statistically significant.

How do you interpret a p-value?

The interpretation of a p-value depends on the context of the study and the specific research question being asked. In general, a smaller p-value suggests stronger evidence against the null hypothesis and supports the alternative hypothesis. It is important to also consider the effect size and other factors when interpreting the results of a hypothesis test.

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