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: Untitled

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: Untitled 2

Confidence Interval for population mean: Untitled 3

  • For Ti-84, go to T Interval on the calculator

Significance Test

Confidence Interval for difference in mean: Untitled 5

  • For Ti-84, go to 2-Sample T Interval on the calculator

Degrees of freedom: Untitled 6

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: Untitled 7

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 <,>, ≠

Untitled + 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