msit test 2
false (type 2 error)
A Type I error occurs when you fail to reject Ho when it should have been rejected. true or false?
outside
But if the Ho value is inside or outside? the interval, there is sufficient evidence to reject Ho, and P-value < α.
smaller
Increasing the sample size will lead to a larger or smaller? standard error (SE), resulting in a larger test statistic. If the test statistic is farther out in the tail, the tail area (P-value) will be smaller.
hypothesis test
Procedure for comparing your sample data with a hypothesis whose truth we question. • Throughout this you assume that is true (even though it may not be). In the conclusion, you will either reject or fail to reject (which isn't really the same as accepting ). Those are the only two conclusions.
sampling variability
different samples will give you different sample statistics.
paired t test
doing all the same things but only changing one variable (which lane they entered) before and after when theres a difference for each The hypotheses for this are based on μD.
p value
helps to make an assumption for null hypothesis Use the theoretical sampling distribution of p-hat under the assumption of the null model to calculate the probability of getting a sample result that extreme. To interpret a blank: Assuming the null hypothesis is true, there is a blank chance of getting a sample result like ours or more extreme.
higher
higher or lower? confidence levels require a wider interval and therefore a greater margin of error
inferential statistics
how can we learn from data? Can you use a sample to make an inference about an entire population?
descriptive statistics
if you have a data set, how can you summarize that data set in meaningful ways? Some descriptive statistics we discussed: the sample mean, the sample standard deviation, the sample median, etc.
decrease
increasing sample size causes p value to increase or decrease?
wider
increasing the confidence level results in a narrower or wider? interval
narrower
increasing the sample size will result in a narrower or wider? interval, as this will shrink the standard error.
x bar
is a sample average. This serves as a point estimate for mu, the unknown population mean. Recall that mu is unknown - our goal is to estimate mu.
y bar
mean from your sample
mu
mean of entire population, true mean
type 2 error
occurs when Ha is true, but we failed to find enough evidence to support it camel cigarettes truly contain more than 1.5 mg of nicotine on average, but we did not find convincing evidence to support this
type 1 error
occurs when Ho is true, but we mistakenly support Ha. camel cigarettes truly contain an average of 1.5 mg of nicotine, but we claimed they had more.
p
parameter of interest for categorical data
mu
parameter of interest for quantitative data
sampling distribution of sample proportion
range of all possible values you might get for p hat
confidence interval
range of values within which we expect the true population proportion to fall.
standard error (SE)
sample standard deviation (s) / square root of sample size (n)
larger
smaller or larger? values of α make it easier to cross the rejection boundary and reject H0 / claim Ha, in other words, easier to claim Ha: μ > 43
Ha
specifies the result we want to claim as correct if is rejected p < default value p > default value p does not equal default value
decrease
standard error will increase or decrease? as the sample size increases
null hypothesis
status quo, initial guess about population parameter
p value
tells us the probability of getting the observed result (or more extreme) under the assumption that is true.
test statistic
tells you how many standard errors the sample proportion falls from the assumed population proportion. (statistic - parameter) / standard deviation of statistic
p value for 2 sample t test
tells you the probability of getting the observed result under the assumption that there is no difference between the two underlying population means.
shape
the blank of the sampling distribution will be approximately normal if np >- 10, and n(1-p) >- 10
mean
the blank of the sampling distribution will be the same as the population proportion. If 30% of business students invest in the stock market, then the mean of the sampling distribution will be 0.30. So, different samples will give different sample proportions and those proportions will be centered around 0.30.
t*
the critical value, serving a purpose similar to that of z*.
margin of error
• The product t* x SE is known as the margin of error. This tells us how much we think our point estimate (x bar) might be off by.
standard error
• The standard deviation of the sampling distribution is the blank. When dealing with proportions, the formula is: where is the population proportion and is the sample size, if the sampled values are independent. (In this context, independence means that one student investing has no effect on any other student deciding to invest.)
sample was randomly selected, at least 10 failures and 10 successes, independent trials (or essentially independent)
3 conditions for calculated confidence interval to be valid
random, nearly normal differences (Thus, either the differences must be normally distributed, or you must have at least 30 pairs of measurements.), independent trials (not independent from each other)
3 conditions for paired t test to be valid
data are independent, random, 10% condition (sample size must be no larger than 10% of the population, nearly normal (population distribution is known to be normal - stated at beginning of problem - or sample size is at least 30)
4 conditions for confidence intervals and results from 2 sample t test to be valid
decrease
Increasing the sample size will increase or decrease? the standard error (SE) since we divide by a larger n, resulting in a narrower interval.
nearly normal
1 of 3 conditions for confidence intervals to be valid If the original data follows a Normal model, then the t-curve will give good results for any sample size. If the original data do not follow a Normal model, then the sample size should be n ≥ 30. Skewed data will be okay as long as n ≥ 30. This can thus be met in one of two ways (only one statement has to be true): (i) The original data must follow a Normal distribution. (ii) The sample size must be n ≥ 30. Note: Unlike proportions, there is no condition for '10 expected successes'. There are no "successes" for means (successes only exist for proportions).
random
1 of 3 conditions for confidence intervals to be valid The data values should be obtained from a blank sample, otherwise they won't represent the population. This should be stated in the problem description.
10%
1 of 3 conditions for confidence intervals to be valid The population must be at least 10 times larger than the sample size. For example, if we take a sample of size 500...is it reasonable to assume the population consists of at least (500)(10) = 5,000 people? Usually this is satisfied.
a
1. How does a 95% confidence interval compare to a 90% confidence interval (assuming everything else remains constant)? a. The 95% CI is wider. b. The 90% CI is wider. c. They are the same.
margin of error
1. In constructing a confidence interval for a proportion, we add and subtract the _________ from the sample proportion.
c
1. Suppose a company is evaluating the effectiveness of a wellness program. Specifically, they sampled 36 employees that took part in the fitness part of the program. They measured their fitness level before and after their participation. Which of the following is true? a. This is a test of two independent means. b. The independence condition (across samples) is violated. c. The independence condition (across samples) is irrelevant. d. The sample size is too small to perform a hypothesis test.
b
1. Suppose you increase the sample size from 100 to 500 (and everything else remains constant). How would this change the confidence interval? a. Wider interval b. Narrower interval c. No change
a
1. Which of the following distinguishes a two-sample t-test for the difference between two means and a paired t-test for the difference in two means? a. Independent Groups b. Randomization c. Nearly Normal Condition
false
A large p-value provides evidence against Ho. true or false?
true
A small p-value provides evidence against Ho. true or false?
true
A small test statistic means p and p hat were not very far apart. true or false?
n - 1
DF =
greater than, less than or equal to
Explain why you must always round up to the next higher whole number when using the formula for n. If we round down, the actual margin of error would be blank the specified margin of error. By rounding up, we ensure that the margin of error will be blank to the desired margin of error.
true
For 95% confidence intervals: The significance level will always be α = 0.05, for both one and two-sided hypothesis tests. true or false?
two tailed
For a one or two-tailed? test of significance, a Test of significance and a Confidence interval will yield the same conclusion!
left tailed
Ha <
right tailed
Ha >
two tailed
Ha does not equal
alternative hypothesis for 2 sample t test
Ha is one of: μ1 - μ2 ≠ 0 (group 1 is different from group 2) μ1 - μ2 < 0 (group 1 is less than group 2) μ1 - μ2 > 0 (group 1 is more than group 2)
inside
If the Ho value is inside or outside? the interval, we cannot reject it: there is insufficient evidence to reject Ho, and we will have P-value > α.
false
If the P-value for a significance test is 0.5, we can conclude that the null hypothesis (H0) is equally likely to be right or wrong. true or false?
standard error
If the question asks about a sample average, use the standard deviation or standard error?
standard deviation
If the question asks about just one randomly selected case, use the standard deviation or standard error?
central limit theorem
If the sample size is large enough, the sampling distribution will be approximately normal. (In this class, "large enough" means the sample size is at least 30.)
true
In running the hypothesis test, we assume Ho is true though it may be false. true or false?
t distribution
It is not common for , the population standard deviation, to be known. When is not known, the standard error can be calculated based on s, the sample standard deviation: However, when s is used in place of , the sampling distribution of the sample mean is no longer Normal. Instead, the blank should be used. Like the Normal distribution, the blank is symmetric and bell-shaped, only the blank has fatter tails:
true
The chance of a confidence interval is determined purely by the confidence level. A 95% confidence will always have 95% confidence of capturing the true value, regardless of sample size. true or false?
false
The margin of error (ME) for a confidence interval in an opinion poll takes into account the fact that some of the questions may be biased. true or false?
wider
The narrower or wider? the interval, the more confident you are that you captured the true proportion
margin of error
The part of the confidence interval formula that follows the sign is known as the blank, which tells you how much you think your estimate of might be off by.)
significance level
The rejection threshold α is called the significance level. The smaller the value of α, the stronger the evidence needed to support . If the situation requires very strong evidence before supporting , then use α = 0.01.
fail to reject
When we have a high p-value we_reject or fail to reject?____ Ho.
reject
When we have a low p-value we __reject__or fail to reject?______ Ho. When the p is low, Ho must go)
2 sample t test
With this, you can compare the means of two independent groups. Comparing TWO Groups or Populations - Take one sample from EACH group (You will have two 's and two sd's) - Compare their means - Is there a significant difference between the two populations? If you have measurements on independent samples, you can use the
false
You can use a confidence interval to conduct a one tailed significance test true or false?
two tailed
You can use a confidence interval to run a one or two tailed? hypothesis test.
Ho
the default assumption, or old value that used to be true null hypothesis
statistically significant
the sample data are unlikely to occur by chance alone if H0 is true
confidence intervals
these estimate population parameter
hypothesis tests
these test population parameters
one tailed
type of test that shows an incentive leads to an increase
essentially independent
used if sampling without replacement The population is at least ten times as large as the sample size. This is known as the 10% condition.
paired t test
used when the measurements on 2 items can be paired into a single value. When you have two sets of measurements on the same people (pre-test and post-test, before and after measurements, etc.), you use this instead of the independent means t-test discussed before. If you have two measurements on the same set of people (or companies, etc.),
sample size
what do you ALWAYS round up for?
degrees of freedom
what does df stand for? DF = n - 1
alternative hypothesis
what we suspect might be true instead
type 2 error
when Ho is false and you fail to reject Ho
correct
when Ho is false and you reject Ho
correct
when Ho is true but fail to reject Ho
type 1 error
when Ho is true but reject Ho
1, 3, 4
which of these should you use for a measure of 2 independent means? H0: μspecial − μregular = 0 vs. Ha: μspecial − μregular ≠ 0 H0: μd = 0 vs. Ha: μd < 0 H0: μspecial − μregular = 0 vs. Ha: μspecial − μregular < 0 H0: μspecial − μregular = 0 vs. Ha: μspecial − μregular > 0 H0: μd = 0 vs. Ha: μd > 0
null hypothesis for 2 sample t test
will always say that there is no difference between the two (unknown) population means: Ho: mu of 1 - mu of 2 = 0