IGNOU MSTL 001 2018 - A packaging process is supposed to fill small boxes of raisins and cla

Question

A packaging process is supposed to fill small boxes of raisins and claimed to fill the boxes with approximately 50 raisins. However, the number of raisins in each box will vary. Suppose 100 boxes of raisins are randomly sampled and the number of raisins in each box is counted. The data are given in the following table:

57	51	53	52	50	60	51	51	52	52
44	53	45	57	39	53	58	47	51	48
49	49	44	54	46	52	55	54	47	53
49	52	49	54	57	52	52	53	49	47
51	48	55	53	55	47	53	43	48	46
54	46	51	48	53	56	48	47	49	57
55	53	50	47	57	49	43	58	52	44
46	59	57	47	61	60	49	53	41	48
59	53	45	45	56	40	46	49	50	57
47	52	48	50	45	56	47	47	48	46

Answer the following:

i) Compute the skewness and kurtosis for the given data and interpret the results.

ii) Compute suitable width of the class interval and construct continuous frequency distribution for the given data.

iii) Also, construct histogram. What does the histogram reveal about the filled boxes?

iv) If the number of raisins in each box is normally distributed, then check whether there is a variation in the number of raisins in boxes at 5 % level of significance?

20 Feb 2018

Answer :

Word Count : 258

From the 100 counts the sample mean is $\bar x=50.64$ raisins and the sample standard deviation is $s=4.672$. Using the moment coefficients, the (Fisher–Pearson) sample skewness is $$ g_1=\frac{\frac{1}{n}\sum (x_i-\bar x)^3}{s^3}\approx 0.019\quad(\text{essentially symmetric}), $$ and the excess kurtosis is $$ g_2=\frac{\frac{1}{n}\sum (x_i-\bar x)^4}{s^4}-3\approx -0.476\quad(\text{platykurtic: flatter peak and lighter tails than normal}). $$ To group the data, the range is $61-39=22$. By Sturges’

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Skip in 10

	Sales (in Rs. ’000)
Store	With sales campaign	Without sales campaign
1	67.2	65.3
2	59.4	54.7
3	80.1	81.3
4	47.6	39.8
5	97.8	92.5
6	38.4	37.9
7	57.3	52.4
8	75.2	69.9
9	94.7	89
10	64.3	58.4
11	31.7	33
12	49.3	41.7
13	54	53.6

57	51	53	52	50	60	51	51	52	52
44	53	45	57	39	53	58	47	51	48
49	49	44	54	46	52	55	54	47	53
49	52	49	54	57	52	52	53	49	47
51	48	55	53	55	47	53	43	48	46
54	46	51	48	53	56	48	47	49	57
55	53	50	47	57	49	43	58	52	44
46	59	57	47	61	60	49	53	41	48
59	53	45	45	56	40	46	49	50	57
47	52	48	50	45	56	47	47	48	46

57	51	53	52	50	60	51	51	52	52
44	53	45	57	39	53	58	47	51	48
49	49	44	54	46	52	55	54	47	53
49	52	49	54	57	52	52	53	49	47
51	48	55	53	55	47	53	43	48	46
54	46	51	48	53	56	48	47	49	57
55	53	50	47	57	49	43	58	52	44
46	59	57	47	61	60	49	53	41	48
59	53	45	45	56	40	46	49	50	57
47	52	48	50	45	56	47	47	48	46

57	51	53	52	50	60	51	51	52	52
44	53	45	57	39	53	58	47	51	48
49	49	44	54	46	52	55	54	47	53
49	52	49	54	57	52	52	53	49	47
51	48	55	53	55	47	53	43	48	46
54	46	51	48	53	56	48	47	49	57
55	53	50	47	57	49	43	58	52	44
46	59	57	47	61	60	49	53	41	48
59	53	45	45	56	40	46	49	50	57
47	52	48	50	45	56	47	47	48	46

57	51	53	52	50	60	51	51	52	52
44	53	45	57	39	53	58	47	51	48
49	49	44	54	46	52	55	54	47	53
49	52	49	54	57	52	52	53	49	47
51	48	55	53	55	47	53	43	48	46
54	46	51	48	53	56	48	47	49	57
55	53	50	47	57	49	43	58	52	44
46	59	57	47	61	60	49	53	41	48
59	53	45	45	56	40	46	49	50	57
47	52	48	50	45	56	47	47	48	46

57	51	53	52	50	60	51	51	52	52
44	53	45	57	39	53	58	47	51	48
49	49	44	54	46	52	55	54	47	53
49	52	49	54	57	52	52	53	49	47
51	48	55	53	55	47	53	43	48	46
54	46	51	48	53	56	48	47	49	57
55	53	50	47	57	49	43	58	52	44
46	59	57	47	61	60	49	53	41	48
59	53	45	45	56	40	46	49	50	57
47	52	48	50	45	56	47	47	48	46

57	51	53	52	50	60	51	51	52	52
44	53	45	57	39	53	58	47	51	48
49	49	44	54	46	52	55	54	47	53
49	52	49	54	57	52	52	53	49	47
51	48	55	53	55	47	53	43	48	46
54	46	51	48	53	56	48	47	49	57
55	53	50	47	57	49	43	58	52	44
46	59	57	47	61	60	49	53	41	48
59	53	45	45	56	40	46	49	50	57
47	52	48	50	45	56	47	47	48	46