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?
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.
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.
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.
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.
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.