Z TEST SCORE

• 1. test


  A statistical procedure used to test an alternative hypothesis against a null hypothesis
• 1. test


  • Used when two samples' means are different, variances are known, and sample is large
• 1. test is a comparison of the means of two independent groups of samples, taken from one populations with known variance
• Null hypothesis


  The hypothesis that is assumed to be true until evidence indicates otherwise
• Alternative hypothesis


  The hypothesis that is proposed to be true
• When performing a statistical test, we are trying to judge the validity of the null hypothesis with an incomplete view of the population
• The larger the sample size, the bigger our window into the population, but there is always a chance our sample will lead us to the wrong conclusion
• When to use Z-test


  • Samples are drawn at random
  • Samples are independent
  • Standard deviation is known
  • Number of observations is large
• Formula for Z-test


  Z = (x̅ - μ) / (σ/√n)
• x̅ = mean of sample, μ = mean of population, σ = standard deviation of population, n = number of observations
• Steps for hypothesis testing

  1. State the null and alternative hypotheses

  2. State the alpha level

  3. Calculate the test statistic (Z-test)

  4. Make the decision to reject or fail to reject the null hypothesis
• Null hypothesis: population mean IQ = 100
• Alternative hypothesis: population mean IQ > 100
• This is a one-tailed test
• Alpha level is 0.05, corresponding to a z-score of 1.645
• Calculation of Z-test statistic


  Z = (112.5 - 100) / (15/√30) = 4.564
• 1. test statistic of 4.564 is greater than 1.645, so we reject the null hypothesis
• Therefore, the principal's claim is supported by the data
• Null hypothesis: average assembly time is 30 minutes
• Alternative hypothesis: average assembly time is not 30 minutes
• This is a two-tailed test
• Alpha level is 0.05, corresponding to a z-score of 1.96
• Calculation of Z-test statistic


  Z = (28 - 30) / (5/√25) = -2
• 1. test statistic of -2 is beyond -1.96, so we reject the null hypothesis
• Therefore, the company's claim is not supported by the data