Final Hacks / Tips
Watch Khan Academy:
● AP College Statistics - Unit 11 (for t* stats)
- On table D for alpha level, if you look up (decimals) it is one sided, but if you look down
(percentage) it is two-sided.
- Eg: 90% means 0.05 is two sided (on both sides 5%) = 1.645 but 95% means 0.025 is
on both sides so it is 0.05 in total = 1.96
- In a t statistic, you do not know the population standard deviation, so to find confidence
intervals you need to use the sample standard deviation (which you calculate) instead,
this is denoted by ‘s’
- Central limit theorem: if your sample size is greater than / equal to 30, the sampling
distribution will be normally distributed, regardless of the population distribution, etc.
- Biased samples can lead to inaccurate results, so they shouldn't be used to create
confidence intervals or carry out significance tests.
- When looking up critical t values in TABLE D, do not forget to account for the degrees of
freedom: df=n-1
- Confidence intervals for t statistics are written as (xbar-, xbar+), eg: (4.86, 8,23)
- Using an example where the interval is (-0.20,0.32): If the entire interval found had been
above [0] (all positive values), or if it had been entirely below [0] (all negative values),
then it would have suggested a difference between the two data sets. BUT the interval
contains 0km—which represents no difference—so it's plausible that there is no
difference between the distances reported by Watch A and Watch B.
- To make a t interval for paired data, instead of xbar, it is the difference in means between
the two pairs and instead of the standard error, it is the difference in standard errors
between the two pairs, the rest of the formula remains the same for calculating
confidence intervals.
- INTERPRETING CIs: A confidence interval for a mean gives us a range of plausible
values for the population mean. If a confidence interval does not include a particular
value, we can say that it is not likely that the particular value is the true population mean.
However, even if a particular value is within the interval, we shouldn't conclude that the
population mean equals that specific value.
When to use z or t stats in significant tests
- When the standard deviation of the population is not given and you have to estimate it
using a standard error, use a t statistic
- If p<a, then you reject the null hypothesis
- If p>a, the you fail to reject the null hypothesis
Watch Khan Academy:
● AP College Statistics - Unit 11 (for t* stats)
- On table D for alpha level, if you look up (decimals) it is one sided, but if you look down
(percentage) it is two-sided.
- Eg: 90% means 0.05 is two sided (on both sides 5%) = 1.645 but 95% means 0.025 is
on both sides so it is 0.05 in total = 1.96
- In a t statistic, you do not know the population standard deviation, so to find confidence
intervals you need to use the sample standard deviation (which you calculate) instead,
this is denoted by ‘s’
- Central limit theorem: if your sample size is greater than / equal to 30, the sampling
distribution will be normally distributed, regardless of the population distribution, etc.
- Biased samples can lead to inaccurate results, so they shouldn't be used to create
confidence intervals or carry out significance tests.
- When looking up critical t values in TABLE D, do not forget to account for the degrees of
freedom: df=n-1
- Confidence intervals for t statistics are written as (xbar-, xbar+), eg: (4.86, 8,23)
- Using an example where the interval is (-0.20,0.32): If the entire interval found had been
above [0] (all positive values), or if it had been entirely below [0] (all negative values),
then it would have suggested a difference between the two data sets. BUT the interval
contains 0km—which represents no difference—so it's plausible that there is no
difference between the distances reported by Watch A and Watch B.
- To make a t interval for paired data, instead of xbar, it is the difference in means between
the two pairs and instead of the standard error, it is the difference in standard errors
between the two pairs, the rest of the formula remains the same for calculating
confidence intervals.
- INTERPRETING CIs: A confidence interval for a mean gives us a range of plausible
values for the population mean. If a confidence interval does not include a particular
value, we can say that it is not likely that the particular value is the true population mean.
However, even if a particular value is within the interval, we shouldn't conclude that the
population mean equals that specific value.
When to use z or t stats in significant tests
- When the standard deviation of the population is not given and you have to estimate it
using a standard error, use a t statistic
- If p<a, then you reject the null hypothesis
- If p>a, the you fail to reject the null hypothesis
