Competed unit 5

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School

Yorkville University *

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Course

2000

Subject

Statistics

Date

Jan 9, 2024

Type

pdf

Pages

189

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STAT 2000 – Unit 5 Carrie Madden Carrie Madden STAT 2000 – Unit 5 1 / 184

Carrie Madden STAT 2000 – Unit 5 2 / 184

Unit 5 – Test for Proportions and Analysis of Categorical Data and Goodness-of-fit Tests Section 1 Unit 5 – Test for Proportions and Analysis of Categorical Data and Goodness-of-fit Tests Carrie Madden STAT 2000 – Unit 5 3 / 184

Unit 5 – Test for Proportions and Analysis of Categorical Data and Goodness-of-fit Tests Review of Inference for a Single Population Proportion P Now suppose we are interested in the proportion ˆ p of successes: ˆ p = X n The mean and standard deviation of ˆ p are µ ˆ p = p and σ ˆ p = ttttttt p ( 1 − p ) n Carrie Madden STAT 2000 – Unit 5 4 / 184

Unit 5 – Test for Proportions and Analysis of Categorical Data and Goodness-of-fit Tests Distribution of a Sample Proportion The Central Limit Theorem says that, if a random variable X represents a sample mean, and if the sample size is high, then the sampling distribution of X is approximately normal. Specifically, Z = X − µ X σ X ∼ N ( 0 , 1 ) But we can think of ˆ p as a kind of sample mean, because we are adding up all the successes we observe and dividing by the sample size n . Carrie Madden STAT 2000 – Unit 5 5 / 184