msit test 2

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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


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