A Type II error would occur if the competitor would not reject the null hypothesis when, in fact, it is false, i.e., if the competitor would not conclude the mean time until the product is received is more than 4 days when, in fact, it is. Assumptions The validity of the results of a hypothesis test depend on certain assumptions and the specific hypothesis test should not be use if these assumptions are not satisfied z-test Assumptions Underlying distribution is normal or the CLT can be One Sample Hypothesis Test assumed to hold (There is a note on the CLT at the end of this section.) Use to see if the population Random sample mean is a specified value or Population standard deviation is known (rarely known) standard. t- test Assumptions Underlying distribution is normal or sample size is large so the CLT can be assumed to hold Random sample z-test Assumptions Two Independent Samples Underlying distribution is normal or the CLT can be assumed to hold Hypothesis Test Random & independently selected samples from 2 populations Use to compare two population Population standard deviation is known means from independent test Assumptions samples Underlying distribution is normal or the CLT can be assumed to hold Random & independently selected samples from 2 populations The variability of the measurements in the two populations is the same and can be measured by a common variance. (Excel offers a t-test that does not make this assumption ) Example: Two-Sample Hypothesis using the t-distribution Problem: For the Salary _ Experience data set, test to see if there is a difference in salaries for employees who selection into their current position was from within the company (internal employees) versus who were selected into their position from outside the company (external employees). Null Hypothesis -   B = H = 0) (The salaries are equal.) (or Alternate Hypothesis -    B Ha: ≠  (The salaries are not equal.) (or ≠ 0) The XL output is as follows.
A Type II error would occur if the competitor would not reject the null hypothesis when, in fact, it is false, i.e., if the competitor would not conclude the mean time until the product is received is more than 4 days when, in fact, it is. Assumptions The validity of the results of a hypothesis test depend on certain assumptions and the specific hypothesis test should not be use if these assumptions are not satisfied One Sample Hypothesis Test Use to see if the population mean is a specified value or standard. z-test Assumptions Underlying distribution is normal or the CLT can be assumed to hold (There is a note on the CLT at the end of this section.) Random sample Population standard deviation is known (rarely known) t- test Assumptions Underlying distribution is normal or sample size is large so the CLT can be assumed to hold Random sample Two Independent Samples Hypothesis Test Use to compare two population means from independent samples z-test Assumptions Underlying distribution is normal or the CLT can be assumed to hold Random & independently selected samples from 2 populations Population standard deviation is known test Assumptions Underlying distribution is normal or the CLT can be assumed to hold Random & independently selected samples from 2 populations The variability of the measurements in the two populations is the same and can be measured by a common variance. (Excel offers a t-test that does not make this assumption ) Example: Two-Sample Hypothesis using the t-distribution Problem: For the Salary _ Experience data set, test to see if there is a difference in salaries for employees who selection into their current position was from within the company (internal employees) versus who were selected into their position from outside the company (external employees). Null Hypothesis H =  (or  - B = 0) (The salaries are equal.) Alternate Hypothesis Ha:  ≠   (or  - B ≠ 0) (The salaries are not equal.) The XL output is as follows.