{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 6.5.q9 - Student Grady Simonton Course Math119 Elementary...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

6.5.q9 - Student Grady Simonton Course Math119 Elementary...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online