Question

You wish to test the following claim ($H_a$) at a significance level of $\alpha = 0.05$. $H_0: \mu = 87.3$ $H_a: \mu \neq 87.3$ You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size $n = 8$ with mean $M = 95$ and a standard deviation of $SD = 15.6$. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... $\circ$ less than (or equal to) $\alpha$ $\circ$ greater than $\alpha$ This p-value leads to a decision to... $\circ$ reject the null $\circ$ accept the null $\circ$ fail to reject the null As such, the final conclusion is that... $\circ$ There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 87.3. $\circ$ There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 87.3. $\circ$ The sample data support the claim that the population mean is not equal to 87.3. $\circ$ There is not sufficient sample evidence to support the claim that the population mean is not equal to 87.3.

          You wish to test the following claim ($H_a$) at a significance level of $\alpha = 0.05$.
$H_0: \mu = 87.3$
$H_a: \mu \neq 87.3$
You believe the population is normally distributed, but you do not know the standard
deviation. You obtain a sample of size $n = 8$ with mean $M = 95$ and a standard deviation of
$SD = 15.6$.
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = 
The p-value is...
$\circ$ less than (or equal to) $\alpha$
$\circ$ greater than $\alpha$
This p-value leads to a decision to...
$\circ$ reject the null
$\circ$ accept the null
$\circ$ fail to reject the null
As such, the final conclusion is that...
$\circ$ There is sufficient evidence to warrant rejection of the claim that the population mean is
not equal to 87.3.
$\circ$ There is not sufficient evidence to warrant rejection of the claim that the population
mean is not equal to 87.3.
$\circ$ The sample data support the claim that the population mean is not equal to 87.3.
$\circ$ There is not sufficient sample evidence to support the claim that the population mean is
not equal to 87.3.

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You wish to test the following claim (Ha) at a significance level of α = 0.05.
H0: μ = 87.3
Ha: μ≠ 87.3
You believe the population is normally distributed, but you do not know the standard
deviation. You obtain a sample of size n = 8 with mean M = 95 and a standard deviation of
SD = 15.6.
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The p-value is...
∘ less than (or equal to) α
∘ greater than α
This p-value leads to a decision to...
∘ reject the null
∘ accept the null
∘ fail to reject the null
As such, the final conclusion is that...
∘ There is sufficient evidence to warrant rejection of the claim that the population mean is
not equal to 87.3.
∘ There is not sufficient evidence to warrant rejection of the claim that the population
mean is not equal to 87.3.
∘ The sample data support the claim that the population mean is not equal to 87.3.
∘ There is not sufficient sample evidence to support the claim that the population mean is
not equal to 87.3.

Added by Beatriz M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

01/11/2024

Step 1

Since we are testing a claim about the population mean (\(\mu\)) and we do not know the population standard deviation, we will use a t-test. The test statistic for a t-test is given by: \[ t = \frac{\bar{x} - \mu}{s/\sqrt{n}} \] where \(\bar{x}\) is the sample Show more…

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You wish to test the following claim (H_(a)) at a significance level of alpha =0.05. H_(0):mu =87.3 H_(a):mu !=87.3 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=8 with mean M=95 and a standard deviation of SD=15.6. What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = ◻ The p-value is... less than (or equal to) alpha greater than alpha This p-value leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 87.3 . There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 87.3. The sample data support the claim that the population mean is not equal to 87.3 . There is not sufficlent sample evidence to support the claim that the population mean is not equal to 87.3 . You wish to test the following clalmHat a significance level ofa=0.05 H=87.3 H87.3 You believe the population is normally distributedbut you do not know the standard deviation.You obtain a sample of size=8with mean M=95and a standard deviation of SD=15.6. What is the p-value for this sample?(Report answer accurate to four decimal places.) p-value= The p-value is... Oless than or equal to Ogreater than This p-value leads to a decision to... Orejeat the null Oaccept the null O fail to reject the null As such,the final conclusion is that... O There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 87.3 O There is not sufficient evidence to warrant rejectlon of the claim that the population mean is not equal to 87.3. O The sample data support the claim that the population mean is not equal to 87.3 O There is not sufficient sample evidence to support the claim that the population mean s not equal to 87.3.

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