Question 1. A software developer has designed two different user interfaces for a program. They want to choose the interface which is easiest to use, and the way that the developer has decided to measure this is by the amount of time it takes a user to nd an important button. The rst option, interface A, was tested on m = 40 randomly chosen individuals. The average time taken to nd the button in that case was 6.875 seconds, with a sample standard deviation of 0.599. The second option, interface B, was tested on 112 = 34 randomly chosen individuals. The average time taken to nd the button in that case was 7.543 seconds. with a sample standard deviation of 0.373. Let pm and p3 denote the true mean time to nd the button for interface A and interface B, respectively. For Question I, use (if is 66.4 where necessary, use a 5% level of signicance, and give your answers correct to three decimal places. (a) State appropriate null and alternative hypotheses. (b) Is this a one-sample or two-sample test? (c) Is this a paired or unpaired test? (6) Calculate the appropriate test statistic by hand. (e) Use the R function qt to calculate the 95% condence interval for the difference in the two means. (1") Use the R function p13 to determine the p-value for the test statistic. (g) State an appropriate conclusion on the basis of your previous answers