Depression and insomnia often go hand-in-hand, and sometimes it is unclear which of the two should be the primary subject of treatment in individuals suffering from insomnia. Mendoza & Company, a national pharmaceutical firm, has positioned itself as a specialist in the production of both antidepressants and sleeping pills. Mendoza's current business model describes the following breakdown of America's approximately 50  million adults suffering from insomnia:  17% use both antidepressants and sleeping pills regularly,  24%  use only antidepressants regularly,  15%  use only sleeping pills regularly, and the remaining  44% use neither antidepressants nor sleeping pills regularly.   A recent issue of the psychiatry journal Patterns contains a study on insomnia. In the study, 200  American adults suffering from insomnia (but otherwise chosen at random) were asked about their use of antidepressants and sleeping pills. The breakdown of their answers is given by the top row of numbers in the table below. (These numbers are the frequencies observed for the sample of  200  insomniacs.) The second row of numbers gives the expected frequenciesunder the hypothesis that Mendoza's model is correct. The bottom row of numbers contains the following value for each of the categories of medication use.   −fOfE2   fE =   −Observed frequencyExpected frequency2   Expected frequency   Part 1 Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your −fOfE2fE  responses to three or more decimal places.   Send data to Excel   Both Only antidepressants Only sleeping pills Neither Total Observed frequency fO fO 40 fO 46 fO 23 fO 91   200 Expected frequency fE fE   fE   fE 30.00 fE 88.00   −fOfE2fE −fOfE2fE   −fOfE2fE   −fOfE2fE 1.633 −fOfE2fE 0.102         Part 2 Answer the following to summarize the test of the hypothesis that Mendoza's model is correct. Use the 0.05  level of significance for the test.   (a)  Determine the type of test statistic to use. Type of test statistic: ▼(Choose one)   (b)  Find the value of the test statistic. (Round your answer to two or more decimal places.)   (c)  Find the critical value. (Round your answer to two or more decimal places.)   (d)Can we conclude that the percentages given in Mendoza's model are incorrect?   Yes     No

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Depression and insomnia often go hand-in-hand, and sometimes it is unclear which of the two should be the primary subject of treatment in individuals suffering from insomnia. Mendoza & Company, a national pharmaceutical firm, has positioned itself as a specialist in the production of both antidepressants and sleeping pills. Mendoza's current business model describes the following breakdown of America's approximately

50

 million adults suffering from insomnia: 

17%

use both antidepressants and sleeping pills regularly, 

24%

 use only antidepressants regularly, 

15%

 use only sleeping pills regularly, and the remaining 

44%

use neither antidepressants nor sleeping pills regularly.

 

A recent issue of the psychiatry journal Patterns contains a study on insomnia. In the study,

200

 American adults suffering from insomnia (but otherwise chosen at random) were asked about their use of antidepressants and sleeping pills. The breakdown of their answers is given by the top row of numbers in the table below. (These numbers are the frequencies observed for the sample of 

200

 insomniacs.) The second row of numbers gives the expected frequenciesunder the hypothesis that Mendoza's model is correct. The bottom row of numbers contains the following value for each of the categories of medication use.

 

−fOfE2
 
fE
=
 
−Observed frequencyExpected frequency2
 
Expected frequency

 

Part 1

Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your

−fOfE2fE

 responses to three or more decimal places.

 

Send data to Excel
  Both Only antidepressants Only sleeping pills Neither Total
Observed frequency
fO

fO
40

fO
46

fO
23

fO
91
 
200
Expected frequency
fE

fE
 

fE
 

fE
30.00

fE
88.00
 
−fOfE2fE
−fOfE2fE
 
−fOfE2fE
 
−fOfE2fE
1.633
−fOfE2fE
0.102
 
 
 
 

Part 2

Answer the following to summarize the test of the hypothesis that Mendoza's model is correct. Use the

0.05

 level of significance for the test.

 

(a)  Determine the type of test statistic to use.
Type of test statistic: ▼(Choose one)
 
(b)  Find the value of the test statistic. (Round your answer to two or more decimal places.)
 
(c)  Find the critical value. (Round your answer to two or more decimal places.)
 
(d)Can we conclude that the percentages given in Mendoza's model are incorrect?
 
Yes
 
 
No
 
 
 

 

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Follow-up Question
Observed
frequency
fo
Expected
frequency
ƒE
(fo-ƒE)²
ƒE
Part 2
Both Only antidepressants
43
0
0
47
0
0
Only sleeping pills
20
30.00
3.333
Neither Total
90
(c) Find the p-value. (Round your answer to three or more decimal places.)
88.00
0.045
(a) Determine the type of test statistic to use.
Type of test statistic: (Choose one) ▼
(b) Find the value of the test statistic. (Round your answer to two or more decimal places.)
200
Answer the following to summarize the test of the hypothesis that Mendoza's model is correct. Use the 0.10 level of significance for the test.
(d) Can we conclude that the percentages given in Mendoza's model are incorrect?
O Yes O No
X
G
X
S
Transcribed Image Text:Observed frequency fo Expected frequency ƒE (fo-ƒE)² ƒE Part 2 Both Only antidepressants 43 0 0 47 0 0 Only sleeping pills 20 30.00 3.333 Neither Total 90 (c) Find the p-value. (Round your answer to three or more decimal places.) 88.00 0.045 (a) Determine the type of test statistic to use. Type of test statistic: (Choose one) ▼ (b) Find the value of the test statistic. (Round your answer to two or more decimal places.) 200 Answer the following to summarize the test of the hypothesis that Mendoza's model is correct. Use the 0.10 level of significance for the test. (d) Can we conclude that the percentages given in Mendoza's model are incorrect? O Yes O No X G X S
Depression and insomnia often go hand-in-hand. Mendoza & Company, a national pharmaceutical firm, has positioned itself as a specialist in the production of
both antidepressants and sleeping pills. Mendoza's current business model describes the following breakdown of America's approximately 50 million adults
suffering from insomnia: 17% use both antidepressants and sleeping pills regularly, 24% use only antidepressants regularly, 15% use only sleeping pills
regularly, and the remaining 44% use neither antidepressants nor sleeping pills regularly.
In a recent study on insomnia in a psychiatry journal, 200 American adults suffering from insomnia (but otherwise chosen at random) were asked about their
use of antidepressants and sleeping pills. The breakdown of their answers is given by the top row of numbers in the table below. (These numbers are the
frequencies observed for the sample of 200 insomniacs.) The second row of numbers gives the expected frequencies under the hypothesis that Mendoza's model
is correct. The bottom row of numbers contains the following value for each of the categories of medication use.
(fo-ƒE)²
JE
Part 1
(Observed frequency - Expected frequency)²
Expected frequency
Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your
to three or more decimal places.
(fo-fE)²
ƒE
responses
Transcribed Image Text:Depression and insomnia often go hand-in-hand. Mendoza & Company, a national pharmaceutical firm, has positioned itself as a specialist in the production of both antidepressants and sleeping pills. Mendoza's current business model describes the following breakdown of America's approximately 50 million adults suffering from insomnia: 17% use both antidepressants and sleeping pills regularly, 24% use only antidepressants regularly, 15% use only sleeping pills regularly, and the remaining 44% use neither antidepressants nor sleeping pills regularly. In a recent study on insomnia in a psychiatry journal, 200 American adults suffering from insomnia (but otherwise chosen at random) were asked about their use of antidepressants and sleeping pills. The breakdown of their answers is given by the top row of numbers in the table below. (These numbers are the frequencies observed for the sample of 200 insomniacs.) The second row of numbers gives the expected frequencies under the hypothesis that Mendoza's model is correct. The bottom row of numbers contains the following value for each of the categories of medication use. (fo-ƒE)² JE Part 1 (Observed frequency - Expected frequency)² Expected frequency Fill in the missing values in the table. Round your responses for the expected frequencies to two or more decimal places. Round your to three or more decimal places. (fo-fE)² ƒE responses
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