Statistics Jeopardy Review

Descriptive Statistics

100

Identify the sampling technique used in the following study:
Calling randomly generated telephone numbers, a
study asked 1001 U.S. adults which medical conditions
could be prevented by their diet.

Simple random sampling

200

This is a zero that implies "nothing".

What is an inherent zero.

300

Draw an ordered stem and leaf plot of the following data:
55 47 51 28
34 39 33 31
40 28 35 68
21 20 42

key 2|3 = 23

2 | 0 1 8 8
3 | 1 3 4 5 9
4 | 0 2 7
5 | 1 5
6 | 8

400

The following data consists of the number of television
sets for a random sample of households:
1 1 0 3 6 1 2 0
What are the mean and standard deviation of the data
(with proper units and significant digits!)

mean: 1.8 sets
standard deviation: 2.0 sets

500

Draw an ogive of the data from above (use 5
classes)--> The number of stories of fifteen notable
buildings in Miami:
55 47 51 28
34 39 33 31
40 28 35 68
21 20 42

->cumulative frequency graph
->check axis labels
->check values:
(14.5,0)
(24.5,4)
(34.5,9)
(44.5,12)
(54.5,14)
(64.5,15)
->roughly "s" shaped

Probability

100

On the basis of prior counts, a quality control
officer says there is a 0.05 probability that a randomly
chosen part is defective. What type of probability is
this an example of?

empirical probability

200

If you toss a coin and then roll a standard die,
what is the probability of getting a head and a number
less than five?

1/3

300

A card is randomly selected from a standard
deck. Event A is selecting a card between 4 and 8
(inclusive). Event B is selecting a club. What is the
probability of Event A or Event B happening?

.538

400

The frequency distribution table shows the number of hits per game played by a baseball player:
Hits  |  Games
0    |   29
1    |   62
2    |   36
3    |   13

Use the frequency distribution to construct a probability distribution and then find the mean and the standard deviation of the probability distribution (units! sig figs!)

x  |  p
0    |   .207
1    |   .443
2    |   .257
3    |   .093

mean is 1.2 hits
standard deviation is .9 hits

500

In a typical day, 31% of people in the U.S. with
Internet access go online to get news. In a random
sample of 3 people in the U.S. with Internet access,
what is the probability that the number going online to
get news is exactly two?

.199

Normal Distribution

100

This is the cut-off value between a "small" sample and a "large" sample.

What is 30

200

The mean rate for satellite television from a sample of
households was $49.00 per month, with a standard
deviation of $2.50 per month. Between what two
values do 99.7% of the data lie? (Assume an
approximately normal distribution)

between $41.50 and $56.50

300

On a dry surface, the braking distance (in meters) of
a Ford Expedition can be approximated by a normal
distribution with a mean of 52 meters and a standard
deviation of 2.5 meters. Find the braking distance
that represents the third quartile? (Use proper units
and number of digits)

54 meters

400

Speeds of vehicles are recorded in front of GCC and
determined to be approximately normally distributed
with a mean of 69.8 mph and a standard deviation of
5.2 mph. Find the percentage of drivers in front of
GCC that are driving between 65 and 75 mph.

66.3%

500

A study found that the mean migration distance of
the green turtle was 2200 kilometers and the
standard deviation was 625 kilometers. Assuming
that the distances are normally distributed, find the
probability that a sample of 12 green turtles has a
mean greater than 2500 kilometers. Would this be
considered unusual?

4.9% Yes, it is unusual.

Confidence Intervals

100

What is the critical value for a 92% confidence
interval with a large sample size and a normally
distributed population?

1.75

200

Construct the indicated confidence interval for the population mean.
c=0.90    x-bar=0.0925    s=0.0013    n=15

because n<30 and the distribution is not normally
distributed, we cannot construct a confidence interval
using either the normal or t-distributions

300

You wish to estimate, with 95% confidence and
within 5% of the true parameter, the proportion of
U.S. adults that think they should be saving more
money. No preliminary estimate of the proportion is
available. Find the minimum sample size needed.

385 people

400

Construct the indicated confidence interval for
the population mean. Assume the data is normally
distributed.
c=0.99    x-bar=10.3    sigma=0.3   n=10

(10.1,10.5)

500

In a random sample of 15 CD players brought in
for repair, the average repair cost was $80 and the
standard deviation was $14. The population is
normally distributed. Construct a 99% confidence
interval for the population mean.

($69,$91)

Hypothesis Testing

100

What are the only two possible
outcomes for a hypothesis test?

1. To reject the null hypothesis
2. To fail to reject the null hypothesis

200

An agriculture cooperative guarantees
that the mean shelf life of a certain type of dried fruit
is at least 400 days. Describe when a type II error
occurs for a hypothesis test of the claim.

A type II error occurs if we fail to reject the claim that the
mean shelf life is at least 400 days, but the mean shelf
life is actually less than 400 days.

300

A soup maker says that the mean of the sodium
content in one serving of a certain soup is no more
than 50 milligrams. What type of hypothesis test is
suggested (tails)?

right-tailed

400

A hat company states that the mean hat size
for a male is at least 7.25. A random sample of 12
hat sizes has a mean of 7.15 and a standard
deviation of 0.27. At alpha=0.05, can you reject the
company's claim that the mean hat size for a male is
at least 7.25? Assume the population is normally
distributed. (state the full conclusion)

(t=-1.28 , t_c=-1.796)
There is not enough evidence
at the 5% level of significance to reject the claim that
the mean hat size for a male is at least 7.25.

500

The U.S. Dept of Agriculture claims that the
mean cost of raising a child from birth to age 2 by
husband-wife families in rural areas is $10,380. A
random sample of 800 children (age 2) has a mean
cost of $10,240 with a standard deviation of $1561.
At alpha=0.05, is there enough evidence to reject
the claim?

(z=-2.54 P-value=.0055 compare to .025, reject H_0)
There is enough evidence
at the 5% level of
significance to reject the claim that
the mean cost
of raising a child from birth to age 2 is $10,380.