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Statistics

Statistics

Question 2.93

Fifteen randomly selected college students were asked to state the numbers of hours they slept the previous night. The resulting data are 5, 6, 6 8, 7, 7, 9, 5, 4, 8, 11, 6, 7, 8, 7. Find the following:

Variance using formula 2.6

Variance using formula 2.10

Standard deviation

Solution

x

(x-µ)

(x-µ)2

5

-1.93

3.74

6

-0.93

0.87

6

-0.93

0.87

8

1.07

1.14

7

0.07

0.00

7

0.07

0.00

9

2.07

4.27

5

-1.93

3.74

4

-2.93

8.60

8

1.07

1.14

11

4.07

16.54

6

-0.93

0.87

7

0.07

0.00

8

1.07

1.14

7

0.07

0.00

Mean (µ)

N = 15

S (x-µ)2

6.93

42.93

Variance using formula 2.6

s2= S (x-µ)2/N

s2 = 42.93/15

s2 = 2.86

Variance using formula 2.10

s2= S (x-µ)2/N-1

s2 = 42.93/15-1

s2= 3.06

Standard deviation

Standard Deviation (s) = v3.06

s = 1.75

Question 1.25

Solution

What is population

Population is all patients who have hypertension and were not included in the study. It may be the total number of patients with hypertension in a particular hospital, community, city, country or the planet.

OR

The population is all persons on the planet with hypertension

What a sample

The group of 5000 selected people for the study is a sample because these 5ooo patients are representing the total number of patients in a certain area or region

Identify parameter of interest

In this scenario, the parameter of interest would be the probability (%) that the drug manufactured by the company have to treat hypertension. In other word, we can say the parameter of interest is to know at what extent the drug is effective to treat hypertension. In simple words “the population is all persons on the planet with hypertension.”

Identify the statistic and give its value

The statistics is the 80% of the individual in this sample that were able to control their hypertension with new drug.

Do we know the value of the parameter?

We can infer that the parameter should be close to the statistic as long as we took an unbiased sample.

Question 2.25

The amounts shown here are the fees charged by quick delivery for the 40 small packages it delivered last Thursday afternoon.

Data

4.03

3.56

6.04

3.16

2.93

3.82

4.3

3.86

4.57

3.59

6.16

5.03

5.46

3.87

6.81

4.91

3.62

3.62

3.7

2.07

3.77

5.77

7.86

4.63

4.81

2.86

5.24

5.44

4.65

3.89

4

2.99

Solution

Stem and leaf display

Stem

Leaf

2

0 8 9 9

3

1 5 5 6 6 7 7 8 8 8 8

4

0 0 3 5 6 6 8 9

5

0 2 4 4 7

6

0 1 8

Distribution of the data

If we draw a curve, then we will come to know that given data is normally distributed and it is positively skewed.

Question 4.53

Location and number of Yum Brand fast Food Stores

USA

Abroad

Total

KFC

5450

7676

13128

Pizza Hut

8306

4680

10986

Taco Bell

5030

193

5223

Long John silver's

1200

33

1233

A&W All-American

485

209

694

Total

18471

12791

31282

Solution

What percent of your location in the United States?

% of location in USA = 18471/31282 = 59%

What percent of your location are abroad?

% of location in abroad = 12791/31282 = 41%

What percent of your stores are pizza hut?

% of store of Pizza Hut = 10986/31282 = 35%

What percent of your stores are taco Bell given that the location in United States?

% of Taco bell (United States) = 5030/31282 = 16%

What percent of your stores are abroad l given that the stores in A&W All-America?

% of store in abroad (given that A&M All- America) = 209/ 31282 = 0.67%

What percent of your stores are KFC given that the location in Abroad?

%KFC given that the location in Abroad = 7676/31282 = 24%

What percent of your abroad locations are KFC

% abroad locations are KFC = 7676/12791 = 60%

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