Hypothesis Testing Homework: Does Your Relationship Support Claim?

In summary, Person x claims that b1 = 5 and this claim is supported by the estimated relationship between b0 and b1. However, the estimated relationship does not lie within the acceptance region, so "H0" is discarded and "Ha" is accepted instead.
  • #1
MaxManus
277
1

Homework Statement


I have used OLS and found that:
b0 = 6,85
b1 = 3,88 with se= 0,1121
n = 20


Person x claims that b1 = 5
Choose an alternative hypothesis. Does your estimated relationship support this claim?
Use a 5 % significance level



The Attempt at a Solution



H0 = b1 = 5
H1 b1!= 5
t((1-a)/2,18) = 2,101

t = ([tex]\overline{x}[/tex] - h0)/se(b1) = (3,88 - 5)/(0.1122) = -9.99


t lies not in the interval +- 2,101 so I reject H0

Is this correct?
 
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  • #2
MaxManus said:

Homework Statement


I have used OLS and found that:
b0 = 6,85
b1 = 3,88 with se= 0,1121
n = 20


Person x claims that b1 = 5
Choose an alternative hypothesis. Does your estimated relationship support this claim?
Use a 5 % significance level



The Attempt at a Solution



H0 = b1 = 5
H1 b1!= 5
t((1-a)/2,18) = 2,101

t = ([tex]\overline{x}[/tex] - h0)/se(b1) = (3,88 - 5)/(0.1122) = -9.99


t lies not in the interval +- 2,101 so I reject H0

Is this correct?


se==? and does "b0 = 6,85" means "b0=6.85"?
 
  • #3
Thanks for replying

Se = standard error

I'm not sure about what you mean with the last question, but b0 was point-estimated to be 6,85 or 6.85 if the comma was what you asked about.
 
  • #4
From what I know of Hypothesis test and student T distribution (from Statistics course which I am still undertaking), your answer is correct ie "t" lies not in the acceptance region but in the left rejection region thus "H0" is discarded and "Ha" is accepted instead.

A very small error that i have noticed is that you were supposed to look for the range of acceptance region corresponding to "significance level =5% " and "degrees of freedom= n-1 =19" where as you seem to have looked it up for degrees of freedom = 20 which is not correct and might result in loss of a few marks in exams even though your answer is still correct.

So
t((1-a)/2,18) = 2.09 .....(At least in the table i posses)

I Hope you are satisfied with my reply.
 
  • #5
Thanks:)
 

Related to Hypothesis Testing Homework: Does Your Relationship Support Claim?

1. What is a hypothesis test?

A hypothesis test is a statistical method used to determine whether there is enough evidence to reject or support a claim about a population based on a sample of data.

2. How do you determine the null and alternative hypotheses?

The null hypothesis (H0) is the default assumption that there is no significant difference or relationship between variables. The alternative hypothesis (Ha) is the claim that is being tested and is usually the opposite of the null hypothesis.

3. What is the significance level in hypothesis testing?

The significance level, also known as alpha (α), is the probability of rejecting the null hypothesis when it is actually true. It is typically set at 0.05 or 5%, meaning there is a 5% chance of rejecting the null hypothesis even if it is true.

4. How do you interpret the p-value in hypothesis testing?

The p-value is the probability of obtaining the observed results or more extreme results if the null hypothesis is true. If the p-value is less than the significance level, it is considered statistically significant and the null hypothesis can be rejected. If the p-value is greater than the significance level, the null hypothesis cannot be rejected.

5. What are the potential errors in hypothesis testing?

The two types of errors that can occur in hypothesis testing are Type I error and Type II error. Type I error is rejecting the null hypothesis when it is actually true, and Type II error is failing to reject the null hypothesis when it is false. The significance level chosen can affect the likelihood of these errors occurring.

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