Unit 7, Inference for Quantitative Data(Mean)
Constructing Confidence Interval
Population Mean
Difference of Two Means
T-Distribution
- Density curve is similar, but greater than normal distribution
- As degrees of freedom increase, the T-distribution becomes more normally curve.
- Degrees of freedom(df)=n-1
T-test stats Formula:
Conditions for estimating population mean
- Random: Random Sampling
- Independence: Assume at least n*10
- Normality: n≥30(CLT), if CLT not met, draw a box plot(No severe skewness or outliers in the graph as the sample size is not big enough)
- If conditions met, state, "All conditions met, use 1 sample T-interval for population mean"
Standard Error for sample mean:
Confidence Interval for population mean:
- For Ti-84, go to T Interval on the calculator
Significance Test
Confidence Interval for difference in mean:
- For Ti-84, go to 2-Sample T Interval on the calculator
Degrees of freedom:
Conditions for estimating diff. in population mean
- Random: Random Sampling
- Independence: Assume at least n1x10 and n2x10
- Normality: n1≥30(CLT) and n2≥30, if CLT not met, draw a box plot for both population(No severe skewness or outliers in the graph as the sample size is not big enough)
- If conditions met, state, "All conditions met, construct 2 sample T-interval for difference in population mean"
'0'= no difference
Ho: no diff.
Ha: diff
- If 0 is captured in the interval, we fail to reject Ho, which means we do not have convincing evidence as their may be a chance that there is a no difference in [context]
- If 0 is not captured in the interval, we reject Ho, which means we have convincing evidence for [context]. There is difference between [context]
Population mean
Difference in means
T Test stats:
Conditions for estimating population mean
- Random: Random Sampling
- Independence: Assume at least n*10
- Normality: n≥30(CLT), if CLT not met, draw a box plot(No severe skewness or outliers in the graph as the sample size is not big enough) - If conditions met, state, "All conditions met, use 1 sample T-test for population mean"
Conditions for estimating diff. in means
- Random: Random Sampling
- Independence: Assume at least n1x10 and n2x10
- Normality: n1≥30(CLT) and n2≥30, if CLT not met, draw a box plot for both population(No severe skewness or outliers in the graph as the sample size is not big enough)
- If conditions met, state, "All conditions met, construct 2 sample T-Test for difference in means"
State:
- P=Estimate the true mean...
- Ho: population mean=0
- Ha: population mean <,>, ≠
+ t cdf(LB:, UB:, df: )
For Ti-84, go to T-Test on the calculator
If P-value > significance level, We fail to reject Ho and there is no convincing evidence for [context]
If P-value < significance level, we reject Ho and there is convincing evidence for [context]
State:
- Pop. mean 1:
- Pop. mean 2:
- Ho: pop. mean 1= pop. mean 2
- Ha: pop. mean 1 <,>, ≠ pop. mean 2
For Ti 84, go to 2-Sample T-Test on the calculator