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Hypothesis Testing

Hypothesis Testing. Population Proportion (  ). Notation. n = sample size. p = population proportion of hits or successes, used in the null hypothesis. q = 1 – p = population proportion of misses or failures. . p = x/n = sample proportion of hits.

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Hypothesis Testing

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  1. Hypothesis Testing Population Proportion ( )

  2. Notation n = sample size p = population proportion of hits or successes, used in the null hypothesis. q = 1 – p = population proportion of misses or failures  p = x/n= sample proportion of hits

  3. Test Statistic for Testing a Claim about a Population Proportion, p  p - p z = pq n

  4. Find the P-value of the Z score. Reject the null hypothesis if the P-value is less than or equal to the significance level  (Reject Ho if P-value <  ) Fail to reject the null hypothesis if the P-value is greater than 

  5. p sometimes is given directly “10% of the observed sports cars are red” is expressed as p = 0.10 (determining the sample proportion of households with cable TV)   p sometimes must be calculated “96 surveyed households have cable TV and 54 do not” is calculated using  x 96 p = = = 0.64 n (96+54)

  6. CAUTION  • When the calculation of p results in a decimal with many places, store the number on your calculator and use all the decimals when evaluating the z test statistic. • Large errors can result from rounding p too much. 

  7. For math fans: Prove  z = p - p pq n x np x - µ x - np n n p - p  z = = = =  pq npq npq n n

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