BYU - Stat 121 - Exam 2
Should we perform a test of If they are trying to refute a claim or looking for an obvious answer
significance or obtain a confidence - should be test of significance
interval estimate?
If they ask for an "estimate" of confidence interval
mean would you use test of
significance or a confidence
interval?
- use for random sample
One Sample T-Test - when we don't know the population standard deviation, we use sample s for
std.dev
- when we do that, we have to word the problem w/in the bounds of a t-test
Is it a one-sided or two-sided test
For one-sample t-test - should be
What conditions need to be 1. randomness in the data collection
checked? 2. normality of the pop or large sample size
1. check if the data came from an SRS or a random sample
How are these conditions 2. check a plot of data or n>30
checked on a one-sample t- (plot of data should show no outliers or strong skewness) - even
test when data doesn't look exactly normal - t-procedure will work
(not exactly normal graph)
Which condition is more important? Randomization - without it our data won't be useful or determine
Randomization or Normality? anything about population or parameter (data won't be valid)
What is the standord error of x-bar? s/square root of n - estimates the standard deviation of a sampling
What does it estimate? distribution of x- bar
What is the value of the t = x-bar - population mu/s divided by square root of n, with
standardized test statistic? degrees of freedom n(sample size) - 1
, need to know the t-statistic and degrees of freedom = n-1 (if p-
What is the p-value from the table? value if off the table, look at the smallest p-value and say it's less
than that p-value < .0005 from the corresponding one-sided or
two-sided row
Under .05 - small percentage we would get the results we did
What is an appropriate (testing the alt hypothesis), if the null hypothesis were true.
interpretations of p- value in Over .05 - large percentage we would get the results we did
context? (testing the alt hypothesis), if the null hypothesiss were true.
No - probability looks at the variability & parameter is fixed.
Probability & Pararmeter & p-value
Probability has nothing to do with p-value
Alpha - a reject hypothesis when hypothesis is correct
power reject hypothesis, when Ho is false
The probability level which forms basis for deciding if results
P-value are statistically significant (not due to chance). prop of obtaining
a sample that is different than the hypothesis or does not
represent the population.
Small p-value - if probability is small - either null hypothesis is
P value = .0005
wrong or we picked a really rare sample
.2 - large p-value - probability of seeing data like this if null
P-value = .05 or above
hypothesis is true, is not uncommon. Supports claim that null
hypothesis is true.
We reject Ho and declare the results statistically significant. "when
If p-value is less than .05, what do we
do? p is low - reject Ho"
What does it mean that the results Means critics of null hypothesis, or ones that support the
are statistically significant? alternative hypothesis, have a valid claim against the original
null hypothesis
Are the conclusions practically Could be, could not - depends who you are
important?
If we reject Ho - only interested in first line of the table or
For conclusions in part n, what error
truth/decision Truth, Ho & Ha
is possible?
Decision - Reject Ho, Fail to Reject Ho
Type 1 error (alpha) Rejecting null hypothesis when it is true
Believing (that the mean breaking strenth is less than 30 pounds) -
State type 1 error in context Ha when, in fact, the (mean breaking strength is 30 pounds) - Ho
(ho was true but we believed the alternative hypothesis instead
Suppose p-value = 0.146, what would p value = 0.146 > 0.05 = a, fail to reject Ho - results are not
you conclude? statistically significant. Data does NOT provide sufficient evidence to
support Ha claim or alternative hypothesis.
What error is possible when failing Type 2 error - we believed Ho is true, when Ha is true (alternative
to reject Ho? hypothesis was true but we believed the first hypothesis or Ho
was true)
Give a 95% confidence interval to What paramater is being stated: population mu - true mean
estimate the true mean breaking breaking strength of brand of fishing line
strength of this brand of fishing
line:
Should we perform a test of If they are trying to refute a claim or looking for an obvious answer
significance or obtain a confidence - should be test of significance
interval estimate?
If they ask for an "estimate" of confidence interval
mean would you use test of
significance or a confidence
interval?
- use for random sample
One Sample T-Test - when we don't know the population standard deviation, we use sample s for
std.dev
- when we do that, we have to word the problem w/in the bounds of a t-test
Is it a one-sided or two-sided test
For one-sample t-test - should be
What conditions need to be 1. randomness in the data collection
checked? 2. normality of the pop or large sample size
1. check if the data came from an SRS or a random sample
How are these conditions 2. check a plot of data or n>30
checked on a one-sample t- (plot of data should show no outliers or strong skewness) - even
test when data doesn't look exactly normal - t-procedure will work
(not exactly normal graph)
Which condition is more important? Randomization - without it our data won't be useful or determine
Randomization or Normality? anything about population or parameter (data won't be valid)
What is the standord error of x-bar? s/square root of n - estimates the standard deviation of a sampling
What does it estimate? distribution of x- bar
What is the value of the t = x-bar - population mu/s divided by square root of n, with
standardized test statistic? degrees of freedom n(sample size) - 1
, need to know the t-statistic and degrees of freedom = n-1 (if p-
What is the p-value from the table? value if off the table, look at the smallest p-value and say it's less
than that p-value < .0005 from the corresponding one-sided or
two-sided row
Under .05 - small percentage we would get the results we did
What is an appropriate (testing the alt hypothesis), if the null hypothesis were true.
interpretations of p- value in Over .05 - large percentage we would get the results we did
context? (testing the alt hypothesis), if the null hypothesiss were true.
No - probability looks at the variability & parameter is fixed.
Probability & Pararmeter & p-value
Probability has nothing to do with p-value
Alpha - a reject hypothesis when hypothesis is correct
power reject hypothesis, when Ho is false
The probability level which forms basis for deciding if results
P-value are statistically significant (not due to chance). prop of obtaining
a sample that is different than the hypothesis or does not
represent the population.
Small p-value - if probability is small - either null hypothesis is
P value = .0005
wrong or we picked a really rare sample
.2 - large p-value - probability of seeing data like this if null
P-value = .05 or above
hypothesis is true, is not uncommon. Supports claim that null
hypothesis is true.
We reject Ho and declare the results statistically significant. "when
If p-value is less than .05, what do we
do? p is low - reject Ho"
What does it mean that the results Means critics of null hypothesis, or ones that support the
are statistically significant? alternative hypothesis, have a valid claim against the original
null hypothesis
Are the conclusions practically Could be, could not - depends who you are
important?
If we reject Ho - only interested in first line of the table or
For conclusions in part n, what error
truth/decision Truth, Ho & Ha
is possible?
Decision - Reject Ho, Fail to Reject Ho
Type 1 error (alpha) Rejecting null hypothesis when it is true
Believing (that the mean breaking strenth is less than 30 pounds) -
State type 1 error in context Ha when, in fact, the (mean breaking strength is 30 pounds) - Ho
(ho was true but we believed the alternative hypothesis instead
Suppose p-value = 0.146, what would p value = 0.146 > 0.05 = a, fail to reject Ho - results are not
you conclude? statistically significant. Data does NOT provide sufficient evidence to
support Ha claim or alternative hypothesis.
What error is possible when failing Type 2 error - we believed Ho is true, when Ha is true (alternative
to reject Ho? hypothesis was true but we believed the first hypothesis or Ho
was true)
Give a 95% confidence interval to What paramater is being stated: population mu - true mean
estimate the true mean breaking breaking strength of brand of fishing line
strength of this brand of fishing
line:
