Please answer the problem in this context if possible (State your assumptions, state the values you know from the problem, H (null) and H(alternative), state T-crit (critical value) and level of significance (p-value), state decision rule, state decision, state conclusion)

1) The population mean waiting time to check out of a supermarket has been 4 minutes. Recently, in an effort to reduce the waiting time, the supermarket has experimented with a system in which infrared cameras use body heat and in-store software to determine how many lanes should be opened. A sample of 100 customers was selected, and their mean waiting time to check out was 3.10 minutes, with a sample standard deviation of 2.5 minutes.

a) At the 0.05 level of significance, using the critical value approach to hypothesis testing, is their evidence that the population mean waiting time to check out is less than 4 minutes?

b) At the 0.05 level of significance, using the p-value approach to hypothesis testing, is their evidence that the population mean waiting time to check out is less than 4 minutes?

c) Interpret the meaning of the p-value in this problem

d) Compare your conclusion in a) and b)

e) Create a 95% confident interval for population mean and interpret it using PH Stat. (please show the steps to do this)