STAT 121 Exam Questions Verified Answers Latest
Update 2025
Define p value - ANS Probability of obtaining a test statistic (or sample statistic) as extreme or
more extreme than what we obtained assuming/if H0 is true
Steps to a One Sample T Test for Means - ANS 1. Hypothesis
2. Check conditions (Normality, randomness)
3. Calculate Test Statistic
4. Find p-value
5. Make conclusions
Steps to One Sample T-confidence Interval for Means and when do you do this test - ANS Do
this for estimating parameter mean when sigma is unknown
1. Define parameter
2. Choose confidence level
3. Check conditions
4. Calculate interval
5. Interpret interval:
-confidence level
-parameter
-interval
Steps for Confidence Intervals - ANS 1. State procedure (i.e. one sample z test for means, two
sample t interval for proportions, one sample t interval for means)
2. Describe parameter of interest in context of problem
3. List & check conditions (normality, randomness)
4. Confidence level & t critical value
5. Calculate interval (x +/- t*[s/sq. root of n])
,6. Interpret interval in context
7. Interpret level of confidence in context
Center, Spread & Shape of Population, Sample, and Sample Distribution - ANS Population:
mu, sigma & shape usually unknown
Sample:
x bar, s, & shape usually unknown but similar to the population
Sampling Distribution:
mu, sigma/sq. root of n, & shape is normal when n>30 according to CLT (approximately
normal); if the population was already normal then the sampling distribution is perfectly
normal
**as n increases, the standard deviation decreases
If the If the Sampling distribution of x-bar is normally distributed then we can use ........ what? -
ANS z-scores and find proportions of the curve!
For Process Control Charts what signifies out of control - ANS There are 9 consecutive sample
means on one side of the population mean
or
A sample mean is outside 3 * sigma/sq. root n from the mean
Three Types of Inference - ANS Point Estimation
Interval Estimation
Hypothesis Test
,When do you use a T procedure - ANS when sigma is unknown
s/sq. root of n
T distribution is __________ and ___________ than a normal distribution
What happens to it when df increases? - ANS wider & shorter
gets closer to normal when df increases
What is margin of error? - ANS The amount we add and subtract from our sample statistic to
get our interval
How do you interpret a 90% confidence level? - ANS 90% of all the intervals we could obtain by
performing the same procedure over and over again would contain the parameter of interest.
How do you interpret a 95% confidence interval? - ANS We are 95% confident (or whatever
level) that the parameter (mean or proportion in context) is between this interval
When sample size changes, what happens to margin of error? - ANS As n increases, margin of
error decreases (more accurate)
When confidence level increases, how does margin of error increase? - ANS Margin of error
increases
How do you find sample size from margin of error? Do you round up or down? - ANS n = (z *
sigma/ m) ^2
Round UP to nearest whole number
Type 1 vs. Type 2 errors: How do you know what is what? - ANS ART is my BFF
Alpha Reject True H0
, Beta Fail to reject False H0
What is alpha & beta and power - ANS α - Probability of Rejecting a H0, when H0 is true
(probability of a Type I error)
β - Probability of a type II error (Failing to reject H0 when it is false)
Power = Probability of correctly rejecting H0 when H0 is false (1 - β)
The t statistic measures - ANS how many standard errors the observed x̄ is from the claimed
parameter value μ
Whenever performing a one sample t procedure on means, we should check for - ANS
randomization and no outliers in the data.
Sample results are said to be statistically significant whenever - ANS the difference between the
observed statistic and the claimed parameter value given in H0 is too large to be due to chance.
The margin of error in a confidence interval covers only which kind of errors? - ANS chance
errors due to random sampling
The purpose of a confidence interval is to provide - ANS plausible values that a parameter could
be.
The weekly oral dosage of anabolic steroids was measured on a sample of 20 body builders. A
95% confidence interval estimate for the average weekly oral dose of anabolic steroids
obtained from these results was 152 mg to 194 mg. What is a correct interpretation of this
confidence interval? - ANS We are 95% confident that the average weekly dose of anabolic
steroids used by all body builders is between 152 mg. and 194 mg.
Update 2025
Define p value - ANS Probability of obtaining a test statistic (or sample statistic) as extreme or
more extreme than what we obtained assuming/if H0 is true
Steps to a One Sample T Test for Means - ANS 1. Hypothesis
2. Check conditions (Normality, randomness)
3. Calculate Test Statistic
4. Find p-value
5. Make conclusions
Steps to One Sample T-confidence Interval for Means and when do you do this test - ANS Do
this for estimating parameter mean when sigma is unknown
1. Define parameter
2. Choose confidence level
3. Check conditions
4. Calculate interval
5. Interpret interval:
-confidence level
-parameter
-interval
Steps for Confidence Intervals - ANS 1. State procedure (i.e. one sample z test for means, two
sample t interval for proportions, one sample t interval for means)
2. Describe parameter of interest in context of problem
3. List & check conditions (normality, randomness)
4. Confidence level & t critical value
5. Calculate interval (x +/- t*[s/sq. root of n])
,6. Interpret interval in context
7. Interpret level of confidence in context
Center, Spread & Shape of Population, Sample, and Sample Distribution - ANS Population:
mu, sigma & shape usually unknown
Sample:
x bar, s, & shape usually unknown but similar to the population
Sampling Distribution:
mu, sigma/sq. root of n, & shape is normal when n>30 according to CLT (approximately
normal); if the population was already normal then the sampling distribution is perfectly
normal
**as n increases, the standard deviation decreases
If the If the Sampling distribution of x-bar is normally distributed then we can use ........ what? -
ANS z-scores and find proportions of the curve!
For Process Control Charts what signifies out of control - ANS There are 9 consecutive sample
means on one side of the population mean
or
A sample mean is outside 3 * sigma/sq. root n from the mean
Three Types of Inference - ANS Point Estimation
Interval Estimation
Hypothesis Test
,When do you use a T procedure - ANS when sigma is unknown
s/sq. root of n
T distribution is __________ and ___________ than a normal distribution
What happens to it when df increases? - ANS wider & shorter
gets closer to normal when df increases
What is margin of error? - ANS The amount we add and subtract from our sample statistic to
get our interval
How do you interpret a 90% confidence level? - ANS 90% of all the intervals we could obtain by
performing the same procedure over and over again would contain the parameter of interest.
How do you interpret a 95% confidence interval? - ANS We are 95% confident (or whatever
level) that the parameter (mean or proportion in context) is between this interval
When sample size changes, what happens to margin of error? - ANS As n increases, margin of
error decreases (more accurate)
When confidence level increases, how does margin of error increase? - ANS Margin of error
increases
How do you find sample size from margin of error? Do you round up or down? - ANS n = (z *
sigma/ m) ^2
Round UP to nearest whole number
Type 1 vs. Type 2 errors: How do you know what is what? - ANS ART is my BFF
Alpha Reject True H0
, Beta Fail to reject False H0
What is alpha & beta and power - ANS α - Probability of Rejecting a H0, when H0 is true
(probability of a Type I error)
β - Probability of a type II error (Failing to reject H0 when it is false)
Power = Probability of correctly rejecting H0 when H0 is false (1 - β)
The t statistic measures - ANS how many standard errors the observed x̄ is from the claimed
parameter value μ
Whenever performing a one sample t procedure on means, we should check for - ANS
randomization and no outliers in the data.
Sample results are said to be statistically significant whenever - ANS the difference between the
observed statistic and the claimed parameter value given in H0 is too large to be due to chance.
The margin of error in a confidence interval covers only which kind of errors? - ANS chance
errors due to random sampling
The purpose of a confidence interval is to provide - ANS plausible values that a parameter could
be.
The weekly oral dosage of anabolic steroids was measured on a sample of 20 body builders. A
95% confidence interval estimate for the average weekly oral dose of anabolic steroids
obtained from these results was 152 mg to 194 mg. What is a correct interpretation of this
confidence interval? - ANS We are 95% confident that the average weekly dose of anabolic
steroids used by all body builders is between 152 mg. and 194 mg.
