[Solved] Statistics 2B

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– ## Assignment2-20252.docx

**## Assignment2-20252.docx**

**Question 1[38 marks]**

1.1 [11]

The Mendelian theory states that the number of a certain type of peas falling into the classifications round and yellow, wrinkled and yellow, round and green, and wrinkled and green should be in the ratio 9:3:3:1. Suppose that 100 such peas revealed 56, 19,17, and 8 in the respective categories. Are these data consistent with the model? Use 0.05 level of significance.

1.2 [16]

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 young adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

| | | | | |
| — | — | — | — | — |
| Person’s Age<br>18-23 yr 24-29 yr 30-35 yr Row Total<br>Movie 18–23 yr 24–29 yr 30–35 yr Row Total |
| Drama | 8 | 15 | 11 | 34 |
| Science fiction | 12 | 10 | 8 | 30 |
| Comedy | 9 | 8 | 12 | 29 |
| Column Total | 29 | 33 | 31 | 93 |

1.3 [11]

The number of accidents experienced by machinists in a certain industry were observed for a fixed period of time, with the results as shown in the companying table. Test, at the 5% level of significance, the hypothesis that data come from a Poisson.

| | |
| — | — |
| Accident per Machinist | Frequency of Observation (number of machinists) |
| 0 | 296 |
| 1 | 74 |
| 2 | 26 |
| 3 | 8 |
| 4 | 4 |
| 5 | 4 |
| 6 | 1 |
| 7 | 0 |
| 8 | 1 |

**Question 2 [40 marks]**

For the following time series

| | | | |
| — | — | — | — |
| **Quarter** | **Year** |
| | 2008 | 2009 | 2010 |
| 1 | 26 | 32 | 34 |
| 2 | 50 | 62 | 70 |
| 3 | 40 | 49 | 50 |
| 4 | 33 | 41 | 15 |

2.1 Compute the 4-period centered moving averages. [4]

2.2 On the same axes, produce two-line graphs comparing the actual time series to the 4-period centered moving average values.
**Use the graph paper**.

(Use 1 cm to represent 10 thousand units on the vertical axis) [4]

2.3
Compute the seasonal indexes. [10]

2.4 De-seasonalise the quarterly time series and interpret the first de-seasonalised value.

[6]

2.5
Use the method of least squares from regression analysis to determine the trend line of best fit. Use the zero-sum method for coding. [10]

2.6 Using the trend line you produced in 2.5, estimate the trend value of the time series for Quarter 3 in year 5. [3]

2.7 Find the seasonally-adjusted trend estimate value for Quarter 3 of year 5. [3]

**Question 3[12 marks]**

The Johnson Wholesale Company manufactures a variety of products. The prices and quanties produced for April 1994 and April 2003 are:

| | | | | |
| — | — | — | — | — |
| | 1994 | 2003 | 1994 Quantity | 2003 Quantity |
| Product | Price (N$) | Price (N$) | Produced | Produced |
| Small motor(each) | 236 | 288 | 1760 | 4259 |
| Scrubbing compound( 5 litres) | 296 | 308 | 86450 | 62949 |
| Nails(per half kg) | 40 | 48 | 9460 | 22370 |

3.1 Use 1994 as the base period to compute and interpret the price relative for 2003 for

**_Small motor_** [2]

3.2 Compute and interpret the quantity relative for
**_Nails_** [2]

3.3 Construct a price index to reflect the overall change in prices of the production of the items for the period 1994 – 2003. Use the Laspeyres approach. Interpret your price index. [4]

3.3 Construct a quantity index to reflect the overall change in quantities of the production of the items for the period 1994 – 2003. Use the Paasche approach. Interpret your index. [4]

**Question 4 [10 marks]**

Assume the following are quarterly sales recorded for the period 2008-2011 of Food Lovers shop (in millions of NS).

| | | |
| — | — | — |
| Year | Quarter | Sales |
| 2008 | 1 | 170 |
| | 2 | 187 |
| | 3 | 196 |
| | 4 | 204 |
| 2009 | 1 | 153 |
| | 2 | 195 |
| | 3 | 162 |
| | 4 | 144 |
| 2010 | 1 | 188 |
| | 2 | 196 |
| | 3 | 150 |
| | 4 | 194 |
| 2011 | 1 | 154 |
| | 2 | 190 |
| | 3 | 159 |
| | 4 | 140 |

4.1 Compute the exponential smoothed sales for

(i) ,

(ii) [4]

4.2 Use the Root mean squares error (RMSE) test to determine which -value produces a better forecast. [6]

**## Assignment2-20252.docx**

**Question 1[38 marks]**

1.1 [11]

The Mendelian theory states that the number of a certain type of peas falling into the classifications round and yellow, wrinkled and yellow, round and green, and wrinkled and green should be in the ratio 9:3:3:1. Suppose that 100 such peas revealed 56, 19,17, and 8 in the respective categories. Are these data consistent with the model? Use 0.05 level of significance.

1.2 [16]

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 young adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

| | | | | |
| — | — | — | — | — |
| Person’s Age<br>18-23 yr 24-29 yr 30-35 yr Row Total<br>Movie 18–23 yr 24–29 yr 30–35 yr Row Total |
| Drama | 8 | 15 | 11 | 34 |
| Science fiction | 12 | 10 | 8 | 30 |
| Comedy | 9 | 8 | 12 | 29 |
| Column Total | 29 | 33 | 31 | 93 |

1.3 [11]

The number of accidents experienced by machinists in a certain industry were observed for a fixed period of time, with the results as shown in the companying table. Test, at the 5% level of significance, the hypothesis that data come from a Poisson.

| | |
| — | — |
| Accident per Machinist | Frequency of Observation (number of machinists) |
| 0 | 296 |
| 1 | 74 |
| 2 | 26 |
| 3 | 8 |
| 4 | 4 |
| 5 | 4 |
| 6 | 1 |
| 7 | 0 |
| 8 | 1 |

**Question 2 [40 marks]**

For the following time series

| | | | |
| — | — | — | — |
| **Quarter** | **Year** |
| | 2008 | 2009 | 2010 |
| 1 | 26 | 32 | 34 |
| 2 | 50 | 62 | 70 |
| 3 | 40 | 49 | 50 |
| 4 | 33 | 41 | 15 |

2.1 Compute the 4-period centered moving averages. [4]

2.2 On the same axes, produce two-line graphs comparing the actual time series to the 4-period centered moving average values.
**Use the graph paper**.

(Use 1 cm to represent 10 thousand units on the vertical axis) [4]

2.3
Compute the seasonal indexes. [10]

2.4 De-seasonalise the quarterly time series and interpret the first de-seasonalised value.

[6]

2.5
Use the method of least squares from regression analysis to determine the trend line of best fit. Use the zero-sum method for coding. [10]

2.6 Using the trend line you produced in 2.5, estimate the trend value of the time series for Quarter 3 in year 5. [3]

2.7 Find the seasonally-adjusted trend estimate value for Quarter 3 of year 5. [3]

**Question 3[12 marks]**

The Johnson Wholesale Company manufactures a variety of products. The prices and quanties produced for April 1994 and April 2003 are:

| | | | | |
| — | — | — | — | — |
| | 1994 | 2003 | 1994 Quantity | 2003 Quantity |
| Product | Price (N$) | Price (N$) | Produced | Produced |
| Small motor(each) | 236 | 288 | 1760 | 4259 |
| Scrubbing compound( 5 litres) | 296 | 308 | 86450 | 62949 |
| Nails(per half kg) | 40 | 48 | 9460 | 22370 |

3.1 Use 1994 as the base period to compute and interpret the price relative for 2003 for

**_Small motor_** [2]

3.2 Compute and interpret the quantity relative for
**_Nails_** [2]

3.3 Construct a price index to reflect the overall change in prices of the production of the items for the period 1994 – 2003. Use the Laspeyres approach. Interpret your price index. [4]

3.3 Construct a quantity index to reflect the overall change in quantities of the production of the items for the period 1994 – 2003. Use the Paasche approach. Interpret your index. [4]

**Question 4 [10 marks]**

Assume the following are quarterly sales recorded for the period 2008-2011 of Food Lovers shop (in millions of NS).

| | | |
| — | — | — |
| Year | Quarter | Sales |
| 2008 | 1 | 170 |
| | 2 | 187 |
| | 3 | 196 |
| | 4 | 204 |
| 2009 | 1 | 153 |
| | 2 | 195 |
| | 3 | 162 |
| | 4 | 144 |
| 2010 | 1 | 188 |
| | 2 | 196 |
| | 3 | 150 |
| | 4 | 194 |
| 2011 | 1 | 154 |
| | 2 | 190 |
| | 3 | 159 |
| | 4 | 140 |

4.1 Compute the exponential smoothed sales for

(i) ,

(ii) [4]

4.2 Use the Root mean squares error (RMSE) test to determine which -value produces a better forecast. [6]