A manufacturer of breakfast cereal makes two claims concerning the weight of the packets they produce....

A manufacturer of breakfast cereal makes two claims concerning the
weight of the packets they produce. The manufacturer claims that
a) The mean is 200g
b) The variance is 0.8g2.
Answer the following questions.
1. To investigate the claims, the weight of a sample of packets
produced in a given shift was measured. The values found are
listed in part (a) of ‘Dataset’, with grams (g) as the unit
of measurement. Carry out appropriate statistical tests on claims (a)
and (b).
2. Several weeks later, a smaller sample of packets as taken and their
weight was measured; the data is listed in part (b) of
‘Dataset’, with grams (g) as the unit of measurement. Use this
data to construct confidence intervals for the mean and variance of
the variable ‘W’, the weight of a packet of cereal.
3. Identify any issues with adding the second set of data to the first
and ‘updating’ the results of part 1.

Part (a)

208.06	201.19	205.61	200.88	194.48	196.53
206.21	200.82	205.86	199.82	196.54	198.60
204.72	197.88	204.67	200.72	199.07	195.57
202.28	197.28	201.27	197.73	195.89	198.16
202.63	198.48	198.34	201.29	194.63	199.24
204.83	196.14	201.12	198.10	191.65	198.96
206.69	198.17	203.46	196.92	195.06	199.44

Part (b)
207.94	199.36	201.16	193.67	196.07	202.28
204.64	202.77	202.33	192.26	199.62	202.93

Solutions

Expert Solution

2. 95% Confidence Interval for the mean of the packets of part (b) is:

	Part B
count	12
mean	200.4192
sample standard deviation	4.5394
sample variance	20.6064
minimum	192.26
maximum	207.94
range	15.68

confidence interval 95.% lower	197.8508
confidence interval 95.% upper	202.9875
margin of error	2.5684
z	1.96

3. As we can see that the mean for the part (b) is more than 200g and if it is added to the data of part (a), it can change the mean of the part (a) which violates its satisfiability of mean of 200g.

orchestra answered 1 year ago

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