Tests of Significance

Tests of Significance - Transcript

Tests of Significance
Suppose we combine four decks of cards and we suspect that they have been tampered with such that the proportion of red cards is less than 0 5
Can we prove it if we look at less than half the deck
Can we convince ourselves if we look at less than half the deck
Draw a sample of two cards Suppose they are both black Are you convinced that the true proportion of red cards is less than 0 5
Draw a sample of 20 cards Suppose 8 are black Are you convinced that the true proportion of red cards is less than 0 5
We still don t know for sure but we can quantify our uncertainty by finding out how unusual the above result would be if the true proportion of red cards were in fact 0 5
We will conduct a in the following way
Define the
p the proportion of red cards in the deck
State the and the
Check the necessary and for constructing a Normal model
Since there are at least 10 successes and 10 failures the population of all cards in the deck is at least 200 and the data came from a random sample
the Normal model is appropriate
the procedure
A 1 proportion z test is appropriate
Calculate the
Obtain the
Make a regarding the
Since the p value is so signifying an unlikely result we the null hypothesis

State your in context
If the true proportion of red cards were 0 5 an observed value of at most 8 would occur in about 2 out of every 1000 samples This is strong evidence that the true proportion of red cards is less than 0 5
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