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Unformatted text preview: Student: Grady Simonton Course: Math119: Elementary Statistics  Spring 2.010  CRN: 492.39
Instructor: Shawn Parvini  16 weeks Date: 3/18/10 Book: Triola: Elementary Statistics, 11e
Time: 4:14 PM Cans of a certain beverage are labeled to indicate that they contain 16 oz. The amounts in a sample of cans are measured and the sample statistics are n = 38 and x = 16.06 oz. If the beverage cans are ﬁlled so that u = 16.00 oz (as labeled) and
the population standard deviation is o = 0.15 oz (based on the sample results), ﬁnd the probability that a sample of 38
cans will have a mean of 16.06 oz or greater. Do these results suggest that the beverage cans are ﬁlled with an amount
greater than 16.00 oz? Since the sample size is greater than 30 and the original population has a mean of u and a standard deviation of o, the
sample means will have a distribution that can be approximated by the normal distribution with a mean of u and a standard deviation of 0' a” E, where n is the sample size. While either technology or a standard normal distribution table can be used to ﬁnd the probability, for the purposes of
this explanation, use a table. First convert the given sample mean, ;= 16.06, to the corresponding z score using the formula below, assuming that the
population mean, u, is equal to 16.00 as labeled. ;u
6 if? Substitute ; = 16.06, [.1 = 16.00, 0 = 0.15, and n = 38 into the formula and simplify, rounding to two decimal places. 2: 16.06 — 16.00
Z = 0.15 Substitute.
\l 38
= 2.41r Simplify. Now use a cumulative standardized normal distribution table to look up the cumulative area under the standard normal
curve to the left of z = 2.47, rounding to four decimal places. The cumulative area is 0.9932. Therefore, the probability that the sample mean is less than 16.06 oz is approximately 0.9932. Subtract this probability
from 1 to ﬁnd the probability that the sample mean is greater than or equal to 16.06 oz. 1 — 0.9932 = 0.0068 The probability that a sample of 38 cans will have a mean of 16.06 oz or greater, given that u = 16.00 and o = 0.15, is
approximately 0.0068. Do these results suggest that the beverage cans are ﬁlled with an amount greater than 16.00 oz? The rare event rule for inferential statistics states that if, under a given assumption, the probability of a particular
observed event is exceptionally small (such as less than 0.05), then conclude that the assumption is probably not correct. In this case, the given assumption is that u = 16.00 oz, and the particular observed event is the sample mean of 16.06 oz Page 1 Student: Grady Silnonton Course: Math119: Elementary Statistics  Spring 2.010  CRN: 49239
Instructor: Shawn Parvini  16 weeks Date: 3/18/10 Book: Triola: Elementary Statistics, 11e
Time: 4:14 PM or greater. The probability of this particular observed event under the given assumption was found to be 0.0068. Use this
information to make a conclusion about the amounts in the beverage cans. Page 2 ...
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