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Performing Hypothesis Tests: Proportions quiz

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  • What are the four main steps in performing a hypothesis test for a population proportion?
    The four steps are: write the hypotheses, calculate the test statistic, find the p-value, and state the conclusion.
  • How do you define the null hypothesis (H0) when testing a population proportion?
    The null hypothesis states that the population proportion is equal to the claimed value, such as H0: p = 0.9.
  • What does the alternative hypothesis (Ha) represent in a hypothesis test for proportions?
    The alternative hypothesis represents what you are testing for, such as Ha: p < 0.9 if you suspect the proportion is less than 0.9.
  • How do you calculate the sample proportion (p̂) in a hypothesis test?
    The sample proportion p̂ is calculated by dividing the number of successes (x) by the sample size (n).
  • What formula is used to calculate the z-score in a population proportion hypothesis test?
    The z-score is calculated as (p̂ - p) divided by the square root of [p(1-p)/n].
  • What does the p-value represent in hypothesis testing?
    The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.
  • How do you determine if a hypothesis test is left-tailed, right-tailed, or two-tailed?
    The direction of the test is determined by the sign in the alternative hypothesis: '<' for left-tailed, '>' for right-tailed, and '≠' for two-tailed.
  • What is the significance level (alpha) in hypothesis testing and how is it used?
    Alpha is the threshold probability for rejecting the null hypothesis; if the p-value is less than alpha, you reject H0.
  • What conclusion do you draw if the p-value is greater than the significance level?
    If the p-value is greater than alpha, you fail to reject the null hypothesis, indicating insufficient evidence for the alternative hypothesis.
  • What are the two conditions that must be met for a valid hypothesis test for a proportion?
    The sample must be random, and both n*p and n*q must be at least 5.
  • How do you calculate n*p and n*q, and what do they represent?
    n*p is the expected number of successes and n*q is the expected number of failures, where q = 1 - p.
  • Why is it important to check that n*p and n*q are both at least 5?
    This ensures the sampling distribution of the sample proportion is approximately normal, which is required for the z-test to be valid.
  • In the example given, what was the sample proportion (p̂) when 172 out of 200 devices passed inspection?
    The sample proportion p̂ was 172 divided by 200, which equals 0.86.
  • If the calculated p-value is 0.029 and the significance level is 0.01, what is the correct decision?
    Since 0.029 > 0.01, you fail to reject the null hypothesis.
  • What does it mean to 'fail to reject the null hypothesis' in the context of a population proportion test?
    It means there is not enough statistical evidence to support the alternative hypothesis about the population proportion.