Question

Suppose you carry out a significance test of H0: μ = 3.5 versus Ha: μ < 3.5 based on sample size n = 17 and obtain t = –3.4. Find the p-value for this test. What conclusion can you draw at the 5% significance level? Explain. (4 points)


Group of answer choices


The p-value is 0.4982. We reject H0 at the 5% significance level because the p-value 0.4982 is greater than 0.05.


The p-value is 0.0018. We reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05.


The p-value is 0.5018. We fail to reject H0 at the 5% significance level because the p-value 0.5018 is greater than 0.05.


The p-value is 0.4982. We fail to reject H0 at the 5% significance level because the p-value 0.4982 is greater than 0.05.


The p-value is 0.0018. We fail to reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05.

Answer 1

Answer:

$t =-3.4$

The degrees of freedom are given by:

$df = n-1= 17-1 =16$

Now we can calculate the p value with this probability:

$p_v =P(t_{16}<-3.4)=0.0018$   And for this case the p value is lower than the significance level and the best conclusion would be:

The p-value is 0.0018. We reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05.

Step-by-step explanation:

Information given

$n=17$ sample size  

$\mu_o =3.5$ represent the value to check

$\alpha=0.05$ represent the significance level

$p_v$ represent the p value

Hypothesis to verify

We want to verify if the true mean for this case is lower than 3.5, the system of hypothesis would be:  

Null hypothesis:$\mu \geq 3.5$  

Alternative hypothesis:$\mu < 3.5$  

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)  

For this case the statistic is given by:

$t =-3.4$

The degrees of freedom are given by:

$df = n-1= 17-1 =16$

Now we can calculate the p value with this probability:

$p_v =P(t_{16}<-3.4)=0.0018$   And for this case the p value is lower than the significance level and the best conclusion would be:

The p-value is 0.0018. We reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05.

Answer 2

Answer:

The p-value is 0.0018. We reject H0 at the 5% significance level because the p-value 0.0018 is less than 0.05.

Step-by-step explanation:

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