Ch. 1/2
Statistic or Parameter: a portion of bikers who have fallen off their bike while riding down a mountain
statistic
What kind of variables are contingency tables used for?
categorical
Flipping a coin twice gives a sample space of...
HH TH HT TT
What is the Zstat for a confidence interval of 95%?
99%?
90%?
95% = 1.96
99% = 2.58
90% = 1.64
Chapter 4
There have been anecdotal reports of the ability of hot towels to remove ticks. In
one experiment conducted, 102 cats were randomly assigned to receive either hot towels
therapy or tick repellent. After two months, the percentage successfully treated was 16% in the
hot towels group and 6% in the tick repellent group
Identify: Response/Explanatory Variable, Experimental Units, Treatments.
Response: Percentage of successfully treated cats
Explanatory: Type of Repellent used (Tick Repellent or Hot Towels)
Experimental Units: Cats
Treatments: Tick repellent/Hot Towels
What is this describing? Based on previously teaching Statistics, Dr. B concluded that the majority of students will pass his class.
Hint (inference or descriptive)
inference
What is the response and explanatory variable for between income and happiness level?
explanatory: income
response: happiness
If
P(A) = 0.8
P(B) = 0.25
P(A and B) = 0
Are they disjoint?
Are they independent?
Why?
Disjoint but NOT Independent
When do we know to use a t-score, and what is the Tstat for a 95% confidence level with a mean of 14 observations?
When population standard deviation is unknown. Only for Sample means, not sample proprotions!
df = 13
Tstat = 2.16
Chapter 6
An exit poll is taken of 3000 voters who voted in favor of a special proposition
designed to lower property taxes and raise the sales tax. Let X denote the number who voted
in favor of a special proposition designed to lower property taxes and raise the sales taxes.
Suppose that in the population, exactly 50% voted for it.
Assuming the conditions of a binomial distribution are met, what is the mean and standard deviation?
Standard Deviation = sqrt[p*(1-p)*n] = 27.39
Gender, Religion, Grade, Etc. are all types of what Variables?
Categorical
Name and explain the 3 different biases in sample surveys.
Extra points if you can give an example for each.
Sampling Bias: occurs from using nonrandom samples or having undercoverage.
Nonresponse Bias: occurs when some sampled subjects cannot be reached or refuse to
participate or fail to answer some questions.
Response Bias: occurs when the subject gives an incorrect response (perhaps lying) or
the way the interviewer asks the questions (or wording of a question in print) is
confusing or misleading.
In a normal distribution, what is the area that falls within 1.04 standard deviations of the mean.
Hint: normalCDF
.7017
Give the general formula for Confidence Interval and give each formula for estimating the sampling distribution of a sample mean and sample proportion
ON BOARD
Chapter 5
A sample of two light bulbs is selected in succession, without replacement, from among 6 good
ones and 4 defective ones. What is the probability of obtaining at least one defective bulb?
p(x) = 0.67
The way observations fall across the range of possible values.
What is the distribution?
Explain the differences between an observational study and a experimental study.
One reason why we'd use one over the other?
Observational: researcher observes values of the
response variable and explanatory variables for the sampled subjects, without anything being
done to the subjects.
Experimental: assign subjects to certain experimental conditions and then observing outcomes on the response variable.
Find the z-score where 82% of the data falls between that z-score.
Hint: invNorm
1.34
A researcher would like to estimate the population proportion of adults living in a
certain country who have at least a high school education. No information is available about its
value. How large a sample size is needed to estimate it within 0.07 with 95% confidence?
When p hat is not given, we assume p hat to be 0.5*
p hat = 0.5
z = 1.96
m = 0.07
n= [p ( 1− p ) z^2]/m^2
n = 196
Chapter 7
A recent poll was taken to gauge the approval of adults for the European currency. Of
the 1000 people sampled in a particular country in the European Union, consider the
sample proportion of people who indicate approval of the euro.
Find the mean and standard deviation of the sampling distribution for this sample
proportion, if the population proportion equals 0.67.
ON BOARD
Name the two types of Quantitative variables, and explain the difference.
Continuous - Measured, intervals
Discrete - Countable, a set of separate numbers
Explain the differences between Simple, Cluster, and Stratified Random Samples
Simple Random Sample: Each possible sample is equally likely
Cluster Random Sample: Identify clusters of subjects, then you take a simple random sample of a portion of those clusters
Stratified Random Sample: Divided population into groups, take simple random sample from EACH group
Flip a coin 20 times. What is the probability that out of those 20 flips, we have exactly 6 tails?
What is the probability that we have at least 6 tails?
hint: Binomial Distribution
Exactly 6: 0.037
At Least 6: 0.979
For a test of H0: p=0.50, the sample proportion is 0.35 based on a sample of 100.
What is the test statistic?
What is the P-Value for Ha: p<0.5?
Reject or Don't reject the null?
a) -3
b) .00135
c) reject the null bc p<0.05
In the past, the mean running time for a certain type of radio battery has been 9.6 hours. The
manufacturer has introduced a change in the production method and wants to perform a
hypothesis test to determine whether the mean running time has changed as a result.
a) Determine the Null and Alternative Hypothesis
b) If the manufacturer INCORRECTLY rejects the null hypothesis and determines there IS in fact a difference between the old and new batteries length of charge (even though in reality there is not), is this a Type I or Type II error?
a)
H0: p = 9.6hrs
Ha: p =/ 9.6hrs
b) Type I Error (false positive)