WEEK 7 HOMEWORK HELPNUMBERS 9,10 & 12
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Find the critical value(s) for a left tailed z test with α = 0.11. Include a graph…
Easy
In Minitab
Graph >> Probability Distribution Plot >> Click View Probability, Click OK
On Menu, Make sure Distribution is set to Normal, Enter 0 as the Mean and 1 as the Standard Deviation
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Continued
On Menu, Make sure Distribution is set to Normal, Enter 0 as the Mean and 1 as the Standard Deviation
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Continued
Click Shaded Area Tab, Click Probability Radial Button, Choose Left Tail, Enter 0.11 as the Probability
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Continued
Click OK button(s), See the Graph
Answer is -1.227, rounded to two
decimals, answer is -1.23
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-1.227
0.11
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Distribution PlotNormal, Mean=0, StDev=1
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Test the claim about the population mean µ, at the given level of significance using the given sample statistics.
Claim: µ = 60, α = 0.05. Sample Statistics: x-bar = 59.1, s = 4.11, n =90
Easy
The claim would be H0 for this one (because it contains equality).
H0: µ = 60
Ha: µ ≠ 60
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Continued
Since Ha: µ ≠ 60 (or contains the not equal to sign), this is a two-tailed test.
You can find the critical values in Minitab. Remember the that α = 0.05.
In Minitab,
Graph >> Probability Distribution Plot >> Click View Probability
Normal Distribution, Mean = 0, Standard Deviation = 1
Click Shaded Area Tab
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Continued
Click Probability button, Click Both Tails button, Enter 0.05 as your probability
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Continued
You can see your Critical values of +/- 1.96 and the rejection region in red.
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-1.960
0.025
1.960
0.025
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Distribution PlotNormal, Mean=0, StDev=1
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Continued
Find your test statistic using Minitab and the specifics of the problem.
Claim: µ = 60, α = 0.05. Sample Statistics: x-bar = 59.1, s = 4.11, n =90
Stat >> Basic Statistics >> 1 Sample Z
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Continued
Click Summarized data button, the specifics including checking Hypothesized Mean box and entering it…
Claim: µ = 60, α = 0.05. Sample Statistics: x-bar = 59.1, s = 4.11, n =90
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Continued
Click Options button and enter confidence. Since α = 0.05, the confidence is 1-0.05 or 0.95 (95%).
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Continued
Print out in Session Window shows test statistic, which is in the rejection region, so REJECT H0: µ = 60 and Accept Ha: µ ≠ 60… Remember you never “Accept the null, you either reject it or “do not reject it.” Also remember the claim can be either…
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-1.960
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1.960
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Distribution PlotNormal, Mean=0, StDev=1
-2.08 is in the rejection region
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H0: µ ≤ 290
Ha: µ > 290 (claim)
The claim in this one is actually since it was “more than 290.” Understand that if they would have said it is “at least 290,” it would have been the null (H0: µ ≥ 290) Always watch the wording
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Continued
Same approach as in number 10 but this one is right tailed…
Why?
Always look at the Ha
Ha: µ > 290 (Pretend it is an arrow, > is “pointing right)
The only time you have two tails is when Ha contains an ≠ sign.
Ha has a >, it’s right tailed. Ha has a <, it’s left tailed.
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In Minitab, they ask us FIRST to find the standardized test statistic z and the corresponding area…
Next Chart…
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Continued
To find the Area, you can use tables or Minitab
In Minitab
Graph >> Probability Distribution Plot > Click View Probability
Normal, Mean of 0, Standard Deviation of 1
Click Shaded Area Tab
CLICK X VALUE RADIAL BUTTON, LEFT TAIL, ENTER VALUE FOR STANDARDIZED TEST STATISTIC
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Continued
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0.8238
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Distribution PlotNormal, Mean=0, StDev=1
They are asking for this area rounded to three decimal places.
So the answer would be 0.824
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Continued
To find the p value, just look at the session window again
This is the p value
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Continued
This can get confusing. But Minitab sorts it out… If you chose the correct values for the hypothesis when using Minitab, it gives you the correct p value.
H0: µ ≤ 290
Ha: µ > 290
The example shows you subtracting the area from 1 or 1 – 0.824 = 0.176 (this is the same p value in your session window).
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Continued
Now compare your p value to your α.
p = 0.176 > α = 0.15
So “p is not less than alpha” - If p is not less than alpha, we do NOT reject.
If “p is less than alpha” – If p is less than alpha, pLess or Please Reject.
That’s the way I remember it…
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