1.2 Hypothesis Testing

• What is the primary purpose of hypothesis testing?

  Reject the null hypothesis
• Hypothesis testing is used to determine if observed results are statistically significant enough to support the alternative
• Hypothesis testing helps researchers make objective decisions about population parameters.
• What does the null hypothesis state in the example of testing the average height of students?

  The average height is175 cm
• The alternative hypothesis in the height example states that the average height is not 175 cm.
• The z-statistic is used when the population standard deviation is known or the sample size is large.
• What is the formula for the z-statistic?

  $z =$$\frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$
• The t-statistic is used when the population standard deviation is unknown and the sample size is small.
• What is the formula for the t-statistic?

  $t =$$\frac{\bar{x} - \mu}{s / \sqrt{n}}$
• Match the test statistic with the population standard deviation requirement:

  z-statistic ↔️ Known

  t-statistic ↔️ Unknown
• The null hypothesis states that there is no significant difference or effect in the population.
• What does the null hypothesis state in the height testing example?

  $\mu =$$175$ cm
• The alternative hypothesis in the height testing example states that $\mu$ is not equal to 175 cm.
• The z-statistic is used when the sample size is greater than or equal to 30.
• What type of data is the chi-square statistic used for?

  Categorical
• The formula for the chi-square statistic is \chi^{2} = \sum \frac{(O - E)^{2}}{E}</latex>.
• What does the significance level represent in hypothesis testing?

  Probability of Type I error
• Common values for the significance level are 0.05, 0.01, and 0.10.
• The two most common test statistics are the z-statistic and the t-statistic
• The z-statistic is used when the population standard deviation is unknown.

  False
• The z-statistic is used when the population standard deviation is known or the sample size is large (n ≥ 30).
• The t-statistic is used when the sample size is greater than 30.

  False
• The t-statistic is used when the population standard deviation is unknown and the sample size is small ($n < 30$).small
• What are the two most common test statistics used in hypothesis testing?

  z-statistic and t-statistic
• The z-statistic is used when the population standard deviation is known
• The t-statistic is used when the population standard deviation is unknown and the sample size is small.
• The formula for the z-statistic is z
• Match the factor with the appropriate statistic:

  Population standard deviation known ↔️ z-statistic

  Small sample size ↔️ t-statistic
• What test statistic should be used if the sample size is 36 and the population standard deviation is known?

  z-statistic
• The formula for the z-statistic is z
• When is the t-statistic used in hypothesis testing?

  Population SD unknown, small n
• The population standard deviation is unknown when using the t-statistic.
• The sample size for using the t-statistic must be less than 30
• Steps to determine the p-value in hypothesis testing

  1️⃣ Calculate the test statistic

  2️⃣ Find the p-value from the relevant distribution
• What is the p-value in hypothesis testing?

  Probability of observed result
• The p-value is calculated using the relevant distribution based on the test statistic.
• What is the assumption made when calculating a p-value about the null hypothesis ($H_{0}$)?


  It is true
• The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true.
• To determine the p-value, the first step is to calculate the test statistic based on the sample data.
• What types of test statistics are commonly used to calculate p-values?

  z-statistic or t-statistic