In: Statistics and Probability
Imagine that you are an expert in Website Analytics, and you have been hired to manage a company’s websites. A successful website is one where visitors come and spend time on the site. More time spent on the site is desirable because you can then convince advertisers to pay you to place their ads on your sites. You have been asked to analyze the performance of the following websites:
1. With 99% confidence, calculate an interval that estimates the
true duration of time a visitor would spend on the WGG site.
2. Test the hypothesis that “visitors do not spend a significant
amount of time on the WGG site.” Would you conclude that this is an
accurate statement?
3. Based on your analysis, would you recommend that advertisers buy
time and space to display their ads on the WGG site? Explain
Let t be the random variable representing the average time spent by customers in the website. Let T be the population average time that visitors spent in the website. let n be sample size and s be population variance.
1. To construct 99% confidence interval that estimates the true duration of time of visitors that would spent on wgc website. Then, P(z1<z<z2)=0.99 where z is standard normal variate having mean 0 and variance 1. Then,P(z1<(t-T)/s/n<z2) =0.99
P(z1×s/n <(t-T)<z2×s/n) =.99
P(t-z1×s/n<T<t+z2×s/n)=0.99
Thus, the required confidence interval is
(t-z1×s/n, t+z2/n) where z1 and z2 are upper and lower values at 99% confidence interval whose values from table are obtained as z1=2.576=z2, thus the 99% confidence interval is:
(t-2.576×s/n, t+2.576×s/n)
2.For our study, the required hypothesis formed can be:
Ho: T=to, the visitors spent minimum significant time in website,
where to minimum significant time required on WGC website.
H1: T<to, the visitors donot spent minimum significant time in website.
The given statements are not accurate, because firstly, in hypothesis testing we are more interested about rejecting the null hypothesis so we prefer taking those statements in null hypothesis which we donot prefer. Secondly, time is generally considered to be a continuous function based on interval so equality at a point is not a very appropriate statement to test.
3.If at 99% confidence interval , null hypothesis is not rejected then we can conclude that visitors do spent sufficient time and space on website. While if Ho is rejected, the claim would be proven wrong and advertising company should not buy time and space to display their ads.
Thanks.