MAT 300 Assignment 1 Bottling Company C
Isaac Farmer
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
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