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Mathematics homework help

Statistics 2B

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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 18-23 yr 24-29 yr 30-35 yr Row Total 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]

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