Question

You pool together two different marketing surveys to see what the willingness to pay for a product is. Survey one has a mean of $20, with standard deviation of 5, and 45 people were surveyed. Survey two has a mean of 30, with standard deviation of 10, and 50 people were surveyed. The null is no difference. The test-statistic, when computed, is 6.06. Would you reject the null?

Answer 1

• Hypothesis to be tested:
  Vs
  where, Population mean of the first marketing survey.
  Population mean of the second marketing survey.
  
• Test Statistics:
  
  
  sample mean of the first marketing survey.
  samplemean of the second marketing survey.
  pooled sample s.d.
  sample size of the first marketing survey.
  sample size of the second marketing survey.
  
• Decision Rule:
  We reject the null hypothesis at level of significance iff
  
  where, is the percentile value of the "t-distribution" with degrees of freedom.   
• Decision:
  
  
  

Since so we reject the null hypothesis at 0.05 level of significance.

I hope this clarifies your doubt. If you're satisfied with the solution, hit the Like button. For further clarification, comment below. Thank You. :)