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?