Prof Anthony Myers

MAT300

03 September 2014

1.

Bottle Number

Ounces (xi) x-xi (x-xi)^2

1

14.5

0.37

0.1369

2

14.6

0.27

0.0729

3

14.7

0.17

0.0289

4

14.8

0.07

0.0049

5

14.9

-0.03

0.0009

6

15.3

-0.43

0.1849

7

14.9

-0.03

0.0009

8

15.5

-0.63

0.3969

9

14.8

0.07

0.0049

10

15.2

-0.33

0.1089

11

15

-0.13

0.0169

12

15.1

-0.23

0.0529

13

15

-0.13

0.0169

14

14.4

0.47

0.2209

15

15.8

-0.93

0.8649

16

14

0.87

0.7569

17

16

-1.13

1.2769

18

16.1

-1.23

1.5129

19

15.8

-0.93

0.8649

20

14.5

0.37

0.1369

21

14.1

0.77

0.5929

22

14.2

0.67

0.4489

23

14

0.87

0.7569

24

14.9

-0.03

0.0009

25

14.7

0.17

0.0289

26

14.5

0.37

0.1369

27

14.6

0.27

0.0729

28

14.8

0.07

0.0049

29

14.8

0.07

0.0049

30

14.6

0.27

0.0729

Mean (x)

14.87

Median

14.8

Standard deviation

0.550329055

2. If x is the mean of a random sample of size n with standard deviation σ, then is a (1-α) 100% confidence interval for the mean of the population.

Therefore, to construct a 95% confidence interval α = .05, n = 30, =1.96, σ = .5503, x = 14.87

Therefore, the interval is

3. We are asked to check the null hypothesis µ = 16 against the alternative hypothesis µ < 16.

So let us apply z-test to check the hypothesis at 0.05 level of significance.

a. H0 : µ = 16 H1: µ < 16 α = .05

b. Reject the null hypothesis if z ≤ -1.645 where t is the value of z0.05 = 1.645 Where

c. x = 14.87, σ = .5503 n = 30, µ = 16 Since -11.25 < -1.645

Therefore, the null hypothesis is rejected.

Hence, the claim that the bottle contains less than 16 ounces of soda is supported.

4. (a.) The three possible causes of this could be: (I) The staff responsible for packaging is not loyal towards their work and using some amount of soda out of every 16 ounces’ bottle for their personal use. (II) The weighing machine is not working properly. (III) The material used for making the bottle is not of good quality which leads to leakage of soda from the bottle during transportation.

Strategies to