Mixing
Changing the null hypothesis in a t-test
$begingroup$
Hello.
I am working on a problem and am confused.
What I know so far is that the two-sided t-test with $alpha=.05$ will reject the null since the $p-$value is smaller.
Here is where I am lost.
The question asks me what to do when the null hypothesis is
$$H_0: mu_1 - mu_2 = 2$$
Intuitively
$$bar{Y_1} - bar{Y_2} = -2$$
so I instantly want to reject the null.
However, I have never seen a situation where the difference between the means are not equal to 0.
How would one approach this problem?
statistics statistical-inference hypothesis-testing confidence-interval
asked Jan 30 at 8:50
hyg17hyg17
2,00222044
$endgroup$
add a comment |
$begingroup$
Hello.
I am working on a problem and am confused.
What I know so far is that the two-sided t-test with $alpha=.05$ will reject the null since the $p-$value is smaller.
Here is where I am lost.
The question asks me what to do when the null hypothesis is
$$H_0: mu_1 - mu_2 = 2$$
Intuitively
$$bar{Y_1} - bar{Y_2} = -2$$
so I instantly want to reject the null.
However, I have never seen a situation where the difference between the means are not equal to 0.
How would one approach this problem?
statistics statistical-inference hypothesis-testing confidence-interval
asked Jan 30 at 8:50
hyg17hyg17
2,00222044
$endgroup$
add a comment |
$begingroup$
Hello.
I am working on a problem and am confused.
What I know so far is that the two-sided t-test with $alpha=.05$ will reject the null since the $p-$value is smaller.
Here is where I am lost.
The question asks me what to do when the null hypothesis is
$$H_0: mu_1 - mu_2 = 2$$
Intuitively
$$bar{Y_1} - bar{Y_2} = -2$$
so I instantly want to reject the null.
However, I have never seen a situation where the difference between the means are not equal to 0.
How would one approach this problem?
statistics statistical-inference hypothesis-testing confidence-interval
asked Jan 30 at 8:50
hyg17hyg17
2,00222044
$endgroup$
Hello.
I am working on a problem and am confused.
What I know so far is that the two-sided t-test with $alpha=.05$ will reject the null since the $p-$value is smaller.
Here is where I am lost.
The question asks me what to do when the null hypothesis is
$$H_0: mu_1 - mu_2 = 2$$
Intuitively
$$bar{Y_1} - bar{Y_2} = -2$$
so I instantly want to reject the null.
However, I have never seen a situation where the difference between the means are not equal to 0.
How would one approach this problem?
statistics statistical-inference hypothesis-testing confidence-interval
statistics statistical-inference hypothesis-testing confidence-interval
asked Jan 30 at 8:50
hyg17hyg17
2,00222044
asked Jan 30 at 8:50
hyg17hyg17
2,00222044
edited Jan 30 at 20:07
hyg17
asked Jan 30 at 8:50
hyg17hyg17
2,00222044
asked Jan 30 at 8:50
hyg17hyg17
2,00222044
asked Jan 30 at 8:50
hyg17hyg17
2,00222044
2,00222044
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Define $Y_3:=Y_2-2$ so the null hypothesis is $mu_1=mu_3,,mu_3:=bar{Y}_3$. Note that subtracting $2$ from one variable shifts its mean while leaving the standard deviation and mean's standard error unchanged. Now you can use an equal-means test.
answered Jan 30 at 20:12
J.G.J.G.
32.6k23250
$endgroup$
$begingroup$
Thank you! So, would it mean that the confidence interval would shift 2 units as well?
$endgroup$
– hyg17
Jan 31 at 19:06
$begingroup$
@hyg17 Yes, when you go from the interval for $mu_1-mu_3$ to that of $mu_1-mu_2$.
$endgroup$
– J.G.
Jan 31 at 22:38
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
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oldest
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active
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$begingroup$
Define $Y_3:=Y_2-2$ so the null hypothesis is $mu_1=mu_3,,mu_3:=bar{Y}_3$. Note that subtracting $2$ from one variable shifts its mean while leaving the standard deviation and mean's standard error unchanged. Now you can use an equal-means test.
answered Jan 30 at 20:12
J.G.J.G.
32.6k23250
$endgroup$
$begingroup$
Thank you! So, would it mean that the confidence interval would shift 2 units as well?
$endgroup$
– hyg17
Jan 31 at 19:06
$begingroup$
@hyg17 Yes, when you go from the interval for $mu_1-mu_3$ to that of $mu_1-mu_2$.
$endgroup$
– J.G.
Jan 31 at 22:38
add a comment |
$begingroup$
Define $Y_3:=Y_2-2$ so the null hypothesis is $mu_1=mu_3,,mu_3:=bar{Y}_3$. Note that subtracting $2$ from one variable shifts its mean while leaving the standard deviation and mean's standard error unchanged. Now you can use an equal-means test.
answered Jan 30 at 20:12
J.G.J.G.
32.6k23250
$endgroup$
$begingroup$
Thank you! So, would it mean that the confidence interval would shift 2 units as well?
$endgroup$
– hyg17
Jan 31 at 19:06
$begingroup$
@hyg17 Yes, when you go from the interval for $mu_1-mu_3$ to that of $mu_1-mu_2$.
$endgroup$
– J.G.
Jan 31 at 22:38
add a comment |
$begingroup$
Define $Y_3:=Y_2-2$ so the null hypothesis is $mu_1=mu_3,,mu_3:=bar{Y}_3$. Note that subtracting $2$ from one variable shifts its mean while leaving the standard deviation and mean's standard error unchanged. Now you can use an equal-means test.
answered Jan 30 at 20:12
J.G.J.G.
32.6k23250
$endgroup$
Define $Y_3:=Y_2-2$ so the null hypothesis is $mu_1=mu_3,,mu_3:=bar{Y}_3$. Note that subtracting $2$ from one variable shifts its mean while leaving the standard deviation and mean's standard error unchanged. Now you can use an equal-means test.
answered Jan 30 at 20:12
J.G.J.G.
32.6k23250
answered Jan 30 at 20:12
J.G.J.G.
32.6k23250
answered Jan 30 at 20:12
J.G.J.G.
32.6k23250
answered Jan 30 at 20:12
J.G.J.G.
32.6k23250
32.6k23250
$begingroup$
Thank you! So, would it mean that the confidence interval would shift 2 units as well?
$endgroup$
– hyg17
Jan 31 at 19:06
$begingroup$
@hyg17 Yes, when you go from the interval for $mu_1-mu_3$ to that of $mu_1-mu_2$.
$endgroup$
– J.G.
Jan 31 at 22:38
add a comment |
$begingroup$
Thank you! So, would it mean that the confidence interval would shift 2 units as well?
$endgroup$
– hyg17
Jan 31 at 19:06
$begingroup$
@hyg17 Yes, when you go from the interval for $mu_1-mu_3$ to that of $mu_1-mu_2$.
$endgroup$
– J.G.
Jan 31 at 22:38
$begingroup$
Thank you! So, would it mean that the confidence interval would shift 2 units as well?
$endgroup$
– hyg17
Jan 31 at 19:06
$begingroup$
Thank you! So, would it mean that the confidence interval would shift 2 units as well?
$endgroup$
– hyg17
Jan 31 at 19:06
$begingroup$
@hyg17 Yes, when you go from the interval for $mu_1-mu_3$ to that of $mu_1-mu_2$.
$endgroup$
– J.G.
Jan 31 at 22:38
$begingroup$
@hyg17 Yes, when you go from the interval for $mu_1-mu_3$ to that of $mu_1-mu_2$.
$endgroup$
– J.G.
Jan 31 at 22:38
add a comment |
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