week 7 homework numbers 9,10 and 12

WEEK 7 HOMEWORK HELPNUMBERS 9,10 & 12

B HeardNot to be copied, posted, shared without my permission. Students can download one copy for their personal use.

WEEK 7 HOMEWORK HELP (MORE)

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


Continued

On Menu, Make sure Distribution is set to Normal, Enter 0 as the Mean and 1 as the Standard Deviation


Continued

Click Shaded Area Tab, Click Probability Radial Button, Choose Left Tail, Enter 0.11 as the Probability


Continued

Click OK button(s), See the Graph

Answer is -1.227, rounded to two

decimals, answer is -1.23

0.4

0.3

0.2

0.1

0.0

X

De

nsit

y

-1.227

0.11

0

Distribution PlotNormal, Mean=0, StDev=1


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

.


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

.


Continued

Click Probability button, Click Both Tails button, Enter 0.05 as your probability

.


Continued

You can see your Critical values of +/- 1.96 and the rejection region in red.

.

0.4

0.3

0.2

0.1

0.0

X

De

nsit

y

-1.960

0.025

1.960

0.025

0



Continued

Find your test statistic using Minitab and the specifics of the problem.


Stat >> Basic Statistics >> 1 Sample Z

.


Continued

Click Summarized data button, the specifics including checking Hypothesized Mean box and entering it…


.


Continued

Click Options button and enter confidence. Since α = 0.05, the confidence is 1-0.05 or 0.95 (95%).

.


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…

.

0.4

0.3

0.2

0.1

0.0

X

De

nsit

y

-1.960

0.025

1.960

0.025

0


-2.08 is in the rejection region


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


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.

.


In Minitab, they ask us FIRST to find the standardized test statistic z and the corresponding area…

Next Chart…


Stat >> Basic Statistics >> 1 Sample Z


Continued

Results

The standardized test statistic z is

0.93


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


Continued

0.4

0.3

0.2

0.1

0.0

XD

en

sit

y0.93

0.8238

0


They are asking for this area rounded to three decimal places.

So the answer would be 0.824


Continued

To find the p value, just look at the session window again

This is the p value


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).

.


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…

.


Continued

Our final conclusion is that we Fail to Reject and say there is not enough evidence to accept our claim. Remember the claim for this one was the alternative because of the wording.

H0: µ ≤ 290

Ha: µ > 290 (claim)

.

week 7 homework numbers 9,10 and 12

Education