Calculator Functions
What does the zoom → 9: ZoomStat function do?
ZoomStat allows you to see graphical representation of your stat plots
What is a sample?
A subset of individuals in the population from which we actually collect data
What are the conditions for a binomial distribution?
B - binary (success or fail)
I - independent
N - number of trials
S - success (how many?)
How do we state what we’re doing for a confidence interval?
"We will use a ___________ interval to estimate, with ___ % confidence, the true (mean/proportion) of __________ ."
In the local middle school, 60% of the students have black hair, 22% have brown hair, 9% have blond hair, 2% have red hair, and 7% have dyed hair. What graph would best represent this data.
Pie chart or Bar Graph
What function of the calculator allows you to find the z* of a confidence level? Use it to find the z-score of confidence level 88%.
invNorm; z* = 1.5547
What are types of sampling bias and response bias? Name 2 for each
Sampling Bias
Undercoverage
Non response bias
Voluntary response bias
Response Bias
Leading questions
Confusing questions
False answers
Why can two mutually exclusive event never be independent?
Mutually exclusive events can still effect each other but independent events cannot.
What is the formula for confidence intervals?
statistic +- critical value*standard deviation of statistic
A certain milk company is suspected of underfilling its cartons of banana milk. The company claims the average amount of milk in each carton contains 10 oz of banana milk with a standard deviation of 0.3 oz. What is the probability that a random sample of 100 cartons produce a sample mean fill of 9.5 oz or less?
Normalcdf (10^-10, 9.5, 10, .3) = 0.04779
What does the LinRegTInt function do?
Provides the confidence interval for linear regression slope coefficient B and computes linear regression T confidence interval for slope coefficient B
Name two types of samples and describe them
Simple Random Sample (SRS)
a subset of a statistical population in which each member of the subset has an equal probability of being chosen
A method of sampling that involves the division of the population into smaller groups (strata)
Cluster Sample
A sampling method that divides a population into separate groups of which a simple random sample is taken of the groups selected
Convenience Sample
Choosing individuals from the population who are easy to reach
In what cases do you use CDF and PDF for binomial and geometric distributions?
PDF is used for exact; CDF is used for inequalities of equal to or fewer
What would happen to the confidence interval if we increase and decrease sample size?
Confidence interval would decrease, and then confidence interval will increase.
Koichi wants to buy stocks from the Speedwagon Foundation. The null hypothesis is that Koichi will make profit. Koichi will make a type I error by doing what? Koichi will make a type II error by doing what?
Type I Error - Koichi decides to not buy in Speedwagon stocks even though it will net him profit. He loses the opportunity to get money.
Type II Error - Koichi decides to buy Speedwagon stocks and he loses money.
Using the calculator, find the interval that has the true proportion with .96 confidence, given the sample size is 1500, and sample proportion is 0.68. Assume all conditions are met. List the steps you did to get your answers.
Found .68 of 1500, which is 1020.
Stat → Tests → 1-PropZInt…
X: 1020 / n: 1500 / C-level 0.96 → calculate
Answer: (0.65526, 0.70474)
Name pros and cons for 1 sample type
Simple Random Sample (SRS)
Pro: every group of n individuals in the population has an equal chance to be selected as the sample
Con: does not work well with large populations
Stratified Random Sample
Pro: Will reduce variability of possible sample results
Con: Cannot be used in all studies since there are several conditions that must be met for it to be used properly. Hence, it is disadvantageous when each member of the population cannot be classified into a subgroup
Cluster Sample
Pro: cheap, quick, and easy. Can easily increase sample size
Con: Least representative of a population of all probability sampling. This technique also has a high possibility of sampling error
Convenience Sample
Pro: quick and easy to get people
Con: very underrepresenting of a population
Voluntary Response
Pro: you get responses; The perfect way of finding people from a specific group
Con: volunteer demand characteristic, volunteer bias
Geometric distributions can also be thought of as what?
Wait time until the first success
Significance test used when testing the claim about the difference between two population means and the population standard deviations are known.
2 samp Z test
Jotaro wants to make a one-sample z interval to estimate the proportion of dolphins in the ocean being bottle-nose. He wants his margin of error to be no more than 0.05 at the 97% confidence interval. What is the smallest sample size required to obtain the the desired margin of error?
A sample size of 471.
Work - 2.17 * sqr (0.5*0.5/n) < = 0.05
Sqr (0.25/n) < = 0.05/2.17
Sqr (0.25)/0.0230414 < = Sqr (n)
471 = n
How to do you find expected counts using the matrix function? List the steps.
(1) Enter data from 2 way table into a matrix [2nd → matrix → edit → choose matrix and enter data corresponding to amount of columns and rows].
(2) Select x^2-Test [Stat → Tests → C: x^2-Test]
(3) Observed should be [A] and Expected should be [B]. Calculate.
(4) Go back to the Matrix function and select B and press enter. Data shown are the expected counts.
A research group designs a study to determine if heavy drinkers die at a younger age. They find that, after many statistical tests, that those who drink excessively are likely to die at a younger age. However, they also find that their non-drinking peers also die at a younger age. What are some confounding variables in this problem that may have resulted in this?
People might eat unhealthy or smoke
Their living conditions/environment is not the best
Family history of disease
What does it mean if X and Y are normally distributed as are X+Y and X-Y?
Use normalCDF
What happens to alpha and beta when power decreases
alpha goes down, beta goes up
A rescue squad of 8 people is to be formed randomly from a group of 12 men and 9 women. Find the probability that the rescue squad will have 5 women and 3 men.
P(5 women and 3 men) = 9C5*12C3 / 21C8 = 0.136222