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Hypothesis Preblems

1. A researcher wishes to test the claim that the average age of lifeguards in Ocean City is greater than 24 years. She selects a sample of 36 guards and finds the mean of the sample to be 24.7 years with a standard deviation of 2 years. Is there evidence to support her claim at a 95% level of confidence?

2. Consider the following situation describing layoffs at a manufacturing plant of the Monsanto Company. Does there appear to be a case of age discrimination between those laid off and those non-laid off?

Employee age layoff status
1 51 no
2 58 no
3 48 no
4 53 yes
5 45 yes
6 43 yes
7 49 no
8 59 no
9 56 yes
10 56 yes
11 54 no
12 55 yes
13 54 no
14 48 no
15 39 no
16 47 no
17 59 yes
18 58 no
19 55 yes
20 57 yes
21 57 yes
22 53 no

(Gregory L. Harper, "Statistics as evidence of age discrimination," The hastings law journal, vol 32, may 1981, pp. 1347-1375)

3. The advisor of an ecology club at a large college expects that the group consists of 10% freshman, 20% Sophomores, 40% Juniors and 30% Seniors. The membership for the club this year is observed to be 14 freshman, 19 sophomores, 51 Juniors and 16 Seniors. At 95% level of confidence, test the advisors belief.

4. In 1978, a small plane slammed into a passenger jet over San Diego, killing 144 people. Langhorne Bond, then the head of the FAA, responded by proposing strict new curbs on small planes around many busy airports.
Examine the following FAA data. Is there a statistically significant difference in the frequency of different types of near midair collisions between the first 6 months of 1985 and the first 6 months of 1986? A corporate plane in this case, means a UPS or FEDEX type of aircraft.

Type of Incident Jan-July '85 Jan-July '86
2 airliners 15 16.6 19 17.4

1 airliner and
1 corporate plane 99 112 130 117

2 corporate planes 262 247.4 244 258.6

TOTAL 376 393

5. In 1987, A consulting organization studying the distribution of disease and acute health problems in California classified the occurrence of stroke within the bay area by the patient's zip code. This allowed a detailed break down of the incidence of stroke in these cities. The following table indicates the rate of hospital admission for stroke in the communities that make up the bay area. Each community is identified by either San Francisco (SF) or other. Is there a difference in the admission for stoke patients in San Francisco than other bay area cities?
(Ramon McLeod, "Pittsburg: Bay Area Sick Spot," San Francisco Chronicle, July 18, p.1)

SF Russian Hill 2.04
SF Ingleside 2.00
Pittsburg 1.98
San Pablo 1.98
Pinole 1.98
Antioch 1.92
SF Marina 1.90
San Jose Center 1.90
SF Potrero 1.89
Oakland 1.88
San Jose East 1.85
Petaluma 1.72
Alameda 1.70
Daily City 1.67
SF Tenderloin 1.55

6. I am sure all of you are familiar with the Scott Peterson (Lacy Peterson Murder Case) case from 2002?

A jury found Scott guilty and he is on death row. One of the major
concerns during this process was whether or not Scott will get a fair
trial. I am sure it was hard to pick a juror who had not heard of the

The trial was to originally take place in Stanislaus County
where the murderer lived and where the crime took place. The newspapers used to say Scott may have a fighting chance if the
Grand Jury is made up of 20 and 30 something adults. There seems to be
this sympathy string he tugs at with this age group. It will be to
Scott's advantage to have a jury predominately made up of jurors in his
generation. Plus, the 20/30 something's make-up a good percentage of the
population in Stanislaus County

Based on the Chi-Square Lecture for Week 4; Does the following data for the Grand Jury in
the Scott Peterson Trial truly support a representation of the
population in Stanislaus County? You must determine if the observed age
distribution of grand jurors and the expected age distribution are
significant or not? This formula is called the Chi-Square.

The IV is age distribution of the (2 categories/Nominal) Grand jurors and
citizens of Stanislaus County. The DV is each age bracket (more than 2

Category Number of Grand Jurors County Wide Distribution by Percentage
21-40 5 42%
41-50 9 23%
51-60 19 16%
61 and Up 33 19%
TOTAL 66 100%