(1)What test would you use in each of the following contexts?

(a)A company has decided to perform a pilot test for its new website's performance. 100 users are provided access to the new website (Experiment group) and the remaining 150 users are still accessing the old website (Control Group). Now you would like to know if there is a significant difference in the performance of these websites.

(b)Compare if two distributions are the same.

(c)Compare the grades of students in three different departments in a University.

(d)A set of 50 people were put on a diet plan and their weights were measured before and after the plan if there is any significant improvement.

(2)A gaming company wants to check the performance of its new User Interface (UI). It has provided the new app with new UI to a random sample of 22000 customers and retained the old UI for the remaining (150,000 customers). Three months after the introduction of new UI, the group with the new UI spent on an average 45.2 minutes per day with a s.d of 6.5 USD while the group with the old UI spent an average of 39 minutes with a s.d of 4.8 USD.

NOTE: Follow all the steps in hypothesis testing. You can use GraphPad for this one.

(a)What is your Null and Alternate Hypothesis? (0.5 point)

(b)Did the new UI result in significantly higher usage of the game app? State the value of the test-statistic, the p-value and the 95% confidence interval.

(c)What do you mean by saying that this is the confidence interval in this case?

(3)A drug was administered to a random sample of 10 patients with high values of Systolic Blood Pressure over a year. The values before and after the drug was administered are given below.

Before After

148 125

142 116

154 130

159 128

157 127

163 134

165 135

158 126

150 125

145 118

(a)what are your null and alternate hypotheses?

(b)What test do you use here?

(c)Was the drug effective in reducing systolic BP significantly?