Download STATISTICS 101: Section L - Homework 7

STATISTICS 101: Section L - Homework 7
Due Friday, April 9, 2004
• Homework is due by 4:00 pm on the due date. You can always turn in your homework
in class.
• You may talk with others about the homework problems but please write your solutions up
independently.
• Please answer homework questions in complete sentences. Make sure to staple the pages of
your assignment together.
• You will have an opportunity to get help on homework during lab.
Reading:
Mar. 26
Apr. 5
- Apr. 2
- Apr. 9
Sections 6.1, 6.2
Section 7.1
Assignment:
1. Statistical methods can be used to decide who wrote specific literary works. Sonnets by an
Elizabethan poet are known to contain an average of µ = 6.9 new words (words not used in
the poet’s other works). The standard deviation of the number of new words is σ = 2.7. A
manuscript with 5 new sonnets has been discovered. Could these newly discovered sonnets
be the work of the Elizabethan poet? The 5 new sonnets contain an average of X = 11.2
words not used in the poet’s known works.
(a) For a random sample of 5 sonnets by the Elizabethan poet, what is the chance that the
sample mean number of new words would be greater than or equal to 11.2?
(b) Use the probability in (a) to argue for, or against, the 5 new sonnets being authored by
the Elizabethan poet.
2. Healthy young adult women have levels of calcium in their blood distributed about a mean of
µ = 9.5 mg/dl with a standard deviation of σ = 0.4 mg/dl. Doctors at a clinic measure the
calcium level of 125 healthy pregnant women at their first prenatal care visit. The sample
mean calcium level is X = 9.46.
(a) Compute the probability that a random sample of 125 healthy young adult women would
have a sample mean calcium level less than or equal to 9.46?
(b) Use the probability in (a) to argue for, or against, the claim that health pregnant women
have the same mean blood calcium level as healthy young adult women.
3. Read pages 414-429 and do exercises 7.2 and 7.4.
4. The local grocery store packages different grades (based on fat content) of hamburger. Usually
the leaner (less fat) grades are more expensive. A random sample of 10 one-pound packages
of hamburger is obtained from the local store and tested for fat content. Below are the
percentage of lean meat for each package.
90.2
94.1
92.0
92.3
91.6
93.2
91.4
92.1
92.4
92.7
(a) Calculate the sample mean percentage lean and the sample standard deviation.
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(b) The packages are labeled 93% lean. Use the summaries in (a) to test the hypothesis
Ho : µ = 93 vs Ha : µ < 93, where µ is the mean percentage lean. Be sure to calculate
the appropriate test statistic and P-value, reach a decision and state a conclusion.
(c) Based on the test in (b), are the packages labeled correctly? Explain briefly.
(d) One of the assumptions for the test in (b) is that the distribution of percentage lean is
normal. Use the sample data to construct a box plot. Does the shape of the box plot
support the assumption of a normal distribution? Explain briefly.
5. A department store randomly selects 100 sales receipts and calculates a sample mean amount
(X=$31.68) and a sample standard deviation (s=$17.42). Based on this random sample, the
store’s manager wishes to make inferences about the population mean sale amount.
(a) Construct a 90% confidence interval for the population mean sale amount.
(b) Originally, the store manager thought that customers spend, on average, $40. Does the
confidence interval support this thought? Explain briefly.
(c) There is a good possibility that the distribution of sales is skewed to the right. Explain
briefly why this might be the case.
(d) If the distribution of sales were skewed to the right, should we be concerned with the
way the interval was constructed in (a)? Explain briefly.
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