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Terms
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- H0: Null Hypothesis
- Population mean=µ Population proportion=Ϭ
- Graphical Tools
- Line chart: trend over time Scatter diagram: relationship between two variables Bar chart: frequency for each category Histogram: frequency for each class of measured data (graph of frequency distr.) Box plot: graphical display based on quartiles, which divide data into 4 parts
- Two-Tailed Tests
- H1: The mean amount of time spent for the Internet is not equal to 5 hours. (µ  5).
- One-Tailed Tests
- H1: The mean yearly salaries earned by full-time employees is more than $45,000. (µ>$45,000)
- Reject Null Hypothesis (H0) If
- Absolute value of test statistic* > critical value* Reject H0 if |Z Value| > critical Z Reject H0 if | t Value| > critical t Reject H0 if p-value < significance level (alpha) Note that direction of inequality is reversed! Reject H0 if very large difference between sample statistic and population parameter in H0
- Type I vs Type II Error
- Alpha=α = P(type I error) = Significance level = probability that you reject true null hypothesis Beta= β = P(type II error) = probability you do not reject a null hypothesis, given H0 false
- Wide Confidence Interval If
- ) small sample size(n) (2) large standard deviation (3) high confidence interval (ex: 99% confidence interval wider than 95% confidence interval) If you want narrow interval, you need a large sample size or small standard deviation or low confidence level.
- Population
- (1) population mean (average number of hours in life of all bulbs) (2) population proportion (% of all bulbs that are defective)
- Qualitative
- Categorical data: success vs. failure ethnicity marital status color zip code 4 star hotel in tour guide
- Quantitative
- Two cases Case 1: discrete Case 2: continuous
- Discrete
- (1) integer values (0,1,2,⬦) (2) example: binomial (3) finite number of possible values (4) counting (5) number of brothers (6) number of cars arriving at gas station
- Continuous
- Real numbers, such as decimal values ($22.22) Examples: Z, t Infinite number of possible values Measurement Miles per gallon, distance, duration of time
- Hypothesis Testing Confidence Intervals
- Quantitative: Mean Qualitative: Proportion