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This is for Psy Statistics class and I'm struggling on how to solve problems like this one below?

 

 Jul 7, 2018

Best Answer 

 #1
avatar+99122 
+1

It has been a long time since I have done stats but I should be able to head you in the right direction.

 

First this site (that I found in our reference material sticky notes) is really useful

http://davidmlane.com/hyperstat/z_table.html

 

\(\sigma=0.5, \qquad \bar x=1.5\;seconds, \qquad n=25 \qquad \alpha=0.1\\~\\ H_o:\;\;\mu=1.8\\ H_A: \;\;\mu<1.8\\ \)

NOTE:

On this graph below I would like to have added a second base lone where the mean is marked at 1.8 and the SD is 0.5.

If I was drawing by hand I would have done this.   But i used the webpage that i sited above :)

*        \(z_{crit}=-2.33\)

 

*         Decision Rule:     If  \(z_{test}<-2.33\qquad reject \quad H_o\)

 

      

                 \(\text{Calculate standard error}\\\sigma_{\bar x}=\frac{\sigma}{\sqrt n}=\frac{0.5}{\sqrt {25}}=\frac{0.5}{5}=0.1 \\ \qquad \text{Note: It is purely coincidental that this is the same as alpha}\\ Z_{test}=\frac{\bar X-\mu}{\sigma_{\bar x}}=\frac{1.5-1.8}{0.1}=\frac{-0.3}{0.1}=-3\\~\\ -3<-2.33 \;\;\;so\;\;\;H_0\;\; is\;\; rejected,\\ H_A \;\;is\;\;accepted \)

 

Conclusion: The hypothesis that the mean population is less than 1.8 is accepted (1% significance level)

This means that there is a less than 1% chance that the exercise program is NOT effective. 

Conclusion: At a 1% significance level it can be concluded that the exercise program IS effective.

 

That should get you started I think.   laugh

 Jul 7, 2018
 #1
avatar+99122 
+1
Best Answer

It has been a long time since I have done stats but I should be able to head you in the right direction.

 

First this site (that I found in our reference material sticky notes) is really useful

http://davidmlane.com/hyperstat/z_table.html

 

\(\sigma=0.5, \qquad \bar x=1.5\;seconds, \qquad n=25 \qquad \alpha=0.1\\~\\ H_o:\;\;\mu=1.8\\ H_A: \;\;\mu<1.8\\ \)

NOTE:

On this graph below I would like to have added a second base lone where the mean is marked at 1.8 and the SD is 0.5.

If I was drawing by hand I would have done this.   But i used the webpage that i sited above :)

*        \(z_{crit}=-2.33\)

 

*         Decision Rule:     If  \(z_{test}<-2.33\qquad reject \quad H_o\)

 

      

                 \(\text{Calculate standard error}\\\sigma_{\bar x}=\frac{\sigma}{\sqrt n}=\frac{0.5}{\sqrt {25}}=\frac{0.5}{5}=0.1 \\ \qquad \text{Note: It is purely coincidental that this is the same as alpha}\\ Z_{test}=\frac{\bar X-\mu}{\sigma_{\bar x}}=\frac{1.5-1.8}{0.1}=\frac{-0.3}{0.1}=-3\\~\\ -3<-2.33 \;\;\;so\;\;\;H_0\;\; is\;\; rejected,\\ H_A \;\;is\;\;accepted \)

 

Conclusion: The hypothesis that the mean population is less than 1.8 is accepted (1% significance level)

This means that there is a less than 1% chance that the exercise program is NOT effective. 

Conclusion: At a 1% significance level it can be concluded that the exercise program IS effective.

 

That should get you started I think.   laugh

Melody Jul 7, 2018
 #2
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+1

laughlaugh Thanks!!

Guest Jul 7, 2018

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