In: Statistics and Probability
. Business owners often rely on experts in search engine optimization to increase the number of people who visit the business website. A study was conducted of 7 comparable small businesses before and after implementing a plan for search engine optimization. The number of visitors per day for each business, based on the day before and after implementing the plan, is shown.
| 
 Business number  | 
 Number of daily visitors before optimization  | 
 Number of daily visitors after optimization  | 
| 
 1  | 
 5389  | 
 5883  | 
| 
 2  | 
 5061  | 
 6189  | 
| 
 3  | 
 5468  | 
 5430  | 
| 
 4  | 
 5579  | 
 6106  | 
| 
 5  | 
 5733  | 
 5534  | 
| 
 6  | 
 4812  | 
 5737  | 
| 
 7  | 
 5834  | 
 5990  | 
(a) Explain the requirements that the data must meet to conduct the hypothesis test described in (b).
(b) Specify the hypotheses for a t-test to see whether the mean number of visitors differs before and after search engine optimization.
(b) Conduct a hypothesis test with a = 0.05, estimating the t-statistic and the p-value.
(c) Report:
the level of significance,
the type and value of the test statistic (including degrees of freedom if appropriate),
the p-value (exact values if possible, or a range of possible values), and
the implications for the null hypothesis.
Do the results indicate that search-engine optimization results in an immediate increase (next day) in the number of visitors to the website?