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M ARIO F . T RIOLA

S TATISTICS. E LEMENTARY. Section 7-5 Testing a Claim about a Proportion. M ARIO F . T RIOLA. E IGHTH. E DITION. The sample is a simple random sample. There is a fixed number of independent trials, two categories of outcomes, and constant probabilities for each trial.

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M ARIO F . T RIOLA

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  1. STATISTICS ELEMENTARY Section 7-5 Testing a Claim about a Proportion MARIO F. TRIOLA EIGHTH EDITION

  2. The sample is a simple random sample. There is a fixed number of independent trials, two categories of outcomes, and constant probabilities for each trial. The normal distribution can be used to approximate the distribution of sample proportions because np  5 and nq 5 are both satisfied. Assumptions

  3. p = population proportion (used in the null hypothesis) q= 1 - p Notation n = number of trials  p = x/n(sample proportion)

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

  5. Reject the null hypothesis if the P-value is less than or equal to the significance level . P-value Method Use the same procedure used on previous hypothesis tests.

  6. (determining the sample proportion of households with cable TV)  p sometimes is given directly “10% of the observed sports cars are red” is expressed as p = 0.10   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)

  7. Claim: p < .27 Example: A survey showed that among 785 randomly selected factory workers, 23.7% smoke. Use a .01 level of significance to test the claim that the rate of smoking among factory workers is less than the 27% rate for the general population. 5. Use 1-PropZTest. .237 x 785 =186.045 Use 186 for x. Graph not necessary for test of proportion P= 0.018 • H0: p ≥ .27 • H1: p < .27 • α = 0.01 • Fail to reject H0 because p > .01 • Normal distribution because n > 30 7. There is not sufficient evidence to support the claim that the rate of smoking among factory workers is less than the 27% rate for the general population.

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