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Lecture 19

# STAT 101 Lecture Notes - Lecture 19: Null Hypothesis, Test Statistic, Sample Size DeterminationPremium

Department

StatisticsCourse Code

STAT 101Professor

Richard WatermanLecture

19This

**preview**shows page 1. to view the full**4 pages of the document.**Stat 101 - Introduction to Business Statistics - Lecture 19: Hypothesis Testing

(continued)

Summary of Testing Process

● Set up the appropriate null and alternative hypothesis

● identify the right test statistic

● calculate the test statistic

● compare the test statistic to the cut off value or compare the pvalue to alpha

○ The cut-off value comes from looking up the appropriate quantile in the t-tables,

but we often round this value to 2 for simplicity when the test is two-sided and α =

0.05.

● if the test statistic exceeds the cut off value or the pvalue is less than alpha, then reject

the null hypothesis

● otherwise, fail to reject the null

Significance Level

● if we use a cut-off value of 2 for the test, then given the null is true there is only a 5%

chance of making a type I error

○ We call this 5% a significance level and write it as α = 0.05

● likewise, if the cutoff value was 1.645 then α = 0.10

One-Sample T-Test for the population Mean

● The test statistic for testing a single mean against a hypothesized value is called the t-

test statistic

● The test is defined as

○

■ n = sample size

■ s = sample standard deviation

■ Xbar = sample mean

■ µ0 = hypothesized value

○ On observing a rare event - ie. Xbar being far from µ0 - we will doubt

assumptions under which it is defined to be rare and thus reject the null

hypothesis

● In JMP..

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