Mathematics, 30.11.2019 02:31 rozlynnv22

Complete parts (a) through (c) below. (a) determine the critical value(s) for a right-tailed test of a population mean at the alphaequals0.10 level of significance with 20 degrees of freedom. (b) determine the critical value(s) for a left-tailed test of a population mean at the alphaequals0.10 level of significance based on a sample size of nequals15. (c) determine the critical value(s) for a two-tailed test of a population mean at the alphaequals0.05 level of significance based on a sample size of nequals12. click here to view the t-distribution area in right tail.

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Answer from: datzmypupppup

a) The critical value on this case would be $t_{crit}=1.325$

b) The critical value on this case would be $t_{crit}=-1.345$

c) The critical values on this case would be $t_{crit}=\pm 2.201$

Step-by-step explanation:

Part a

The system of hypothesis on this case would be:

Null hypothesis: $\mu \leq \mu_0$

Alternative hypothesis: $\mu \mu_0$

Where $\mu_0$ is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, on this case that is given df=20. Since its an upper tailed test we need to find a value a such that:

$P(t_{20}a) = 0.1$

And we can use excel in order to find this value with this function: "=T.INV(0.9,20)". The 0.9 is because we have 0.9 of the area on the left tail and 0.1 on the right.

The critical value on this case would be $t_{crit}=1.325$

Part b

The system of hypothesis on this case would be:

Null hypothesis: $\mu \geq \mu_0$

Alternative hypothesis: $\mu < \mu_0$

Where $\mu_0$ is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, given by:

df=n-1=15-1=14

Since its an lower tailed test we need to find b value a such that:

$P(t_{14}$

And we can use excel in order to find this value with this function: "=T.INV(0.1,14)". The 0.1 is because we have 0.1 of the area accumulated on the left of the distribution.

The critical value on this case would be $t_{crit}=-1.345$

Part c

The system of hypothesis on this case would be:

Null hypothesis: $\mu = \mu_0$

Alternative hypothesis: $\mu \neq \mu_0$

Where $\mu_0$ is the value that we want to test.

In order to find the critical value we need to find first the degrees of freedom, given by:

df=n-1=12-1=11

Since its a two tailed test we need to find c value a such that:

$P(t_{11}c) = 0.025$ or $P(t_{11}$

And we can use excel in order to find this value with this function: "=T.INV(0.025,11)". The 0.025 is because we have 0.025 of the area on each tail.

The critical values on this case would be $t_{crit}=\pm 2.201$

Answer from: Quest

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )

Answer from: Quest

16.80 times .20= 3.36

step-by-step explanation:

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Complete parts (a) through (c) below. (a) determine the critical value(s) for a right-tailed test of...