Download Statistics Using the TI-83 Graphics Calculator Hypothesis Testing

Statistics Using the TI-83 Graphics Calculator
By Mike Koehler
Blue Valley North High School
Overland Park, KS
[email protected]
Page 1 of 5
Statistics Using the TI-83 Graphics
Calculator
Hypothesis Testing
Problem 20: A certain type of children's pain reliever states that it contains 325 mg of
acetaminophen in each ounce of the drug. If 70 one ounce samples are tested for
acetaminophen and it is determined that the mean is 319 mg of the drug and a standard
deviation of 26 mg. With a = .01, test the claim that the population mean is equal to 325
mg.
Problem 21: A test is designed to determine if the right hand of right handed people is
stronger than their left hand. Nine right handed adults were selected and hand strength
tested for each hand. The hand strengths in pounds for each person are given below.
Problem 22: A school wants to compare the ACT scores of those students who complete
a college core of courses (4 years of English, and at least 3 years of Math, Social Science,
and Natural Science) to the scores of those who do not complete this core. The results of a
recent administration of the test follow.
2/14/97
3:02:59 PM
Statistics Using the TI-83 Graphics Calculator
Page 2 of 5
Determine whether completing the core courses produces a higher score on the sub-tests.
Problem 23: Cuckoos lay their eggs in the nests of other birds. Some biologists speculate
that the size of the cuckoo's eggs might be different depending on whether the eggs are laid
in warbler's nests or wren's nests. To check this, biologists searched a wildlife refuge for
warbler's and wren's nests. Summary statistics for the lengths (in mm) of cuckoo's eggs
found in these nests are shown below.
Does this data support the biologists' claim that the size of the eggs differ depending on
whether they are laid in warbler's nests or wren's nests?
( Advanced Placement Course Description, Preliminary Edition; The College Board,
1995)
Problem 24: It is believed that at least 70% of the homes in a city have smoke detectors
installed. Would you agree with this claim if a random survey of homes in the city shows
that 153 of the 240 homes surveyed have working smoke detectors installed?
Problem 25: A vote is to be taken among the residents of a state to determine whether
casino gambling should be legalized. Many voters in the out-state areas feel it will pass
because of the large proportion of city and suburban voters who favor the amendment. To
determine if there is a significant difference in the proportion of metropolitan voters and
out-state voters favoring the proposal, a poll is taken. If 123 of 210 town voters favor the
legalization, and 244 of 515 out-state residents favor it, would you agree that the
2/14/97
3:03:00 PM
Statistics Using the TI-83 Graphics Calculator
Page 3 of 5
proportion of metropolitan voters favoring the proposal is higher than the proportion of
out-state voters? Do you think the proposal will pass?
Problem 26: A national pizza chain recently test marketed a new type of pizza in a large
metropolitan area. It is important for the company to evaluate the product's performance
during this time. This was done in part by sampling consumers and assessing their exposure
to the product. The company selected random samples of consumers from different age
groups and obtained the following results.
Do these data indicate that market penetration is independent of age?
Problem 27: The following data is obtained from a random sample of absences from a
company. At the .05 level of significance, test the claim that the absences occur with equal
frequency on each of the 5 days.
X2cdf computes the cumulative probability function.
The syntax is ( lowerbound, upperbound, degrees of freedom ) .
2/14/97
3:03:00 PM
Statistics Using the TI-83 Graphics Calculator
Page 4 of 5
Problem 28: Does your life expectancy depend on where you live? The following table
gives the state-by-state list of average life expectancy at birth as compiled by the National
Center for Health Statistics. Is there a significant difference in a person's average life
expectancy based on the region of the country in which they live?
Analysis of Variance provides the methods for comparing the means of more than two
populations. In this case we use a one-way ANOVA because we are comparing the means
of populations that are classified in one way, by region of the country. The procedures for
comparing the means involves analyzing the variation in the sample data relative to the
variation in sample means. If the variation in sample means is large relative to the variation
within sample means, the we conclude that the means of the population are not all equal.
2/14/97
3:03:01 PM
Statistics Using the TI-83 Graphics Calculator
Page 5 of 5
Copyright 1996 by Mike Koehler
Statistics Using the TI-83 Graphics Calculator
TI-82 / 83 Activities for Statistics / Probability
Classroom Activities Matrix
(c) Copyright 1997 Texas Instruments Incorporated. All rights reserved.
Trademarks
2/14/97
3:03:01 PM