In the past, the time spent by customers in a certain shop had mean 10.5 minutes and standard deviation4.2 minutes. Following a change of layout in the shop, the mean

time spent in the shop by a random sampleof 50 customers is found to be 12.0 minutes. Assuming that the standard deviation is unchanged, test at the 1% significance level whether the meantime spent by customers in the shop has changed.171 i) Another random sample of 50 customers is chosen and a similar test at the 1% significance level is carried out. Given that the population mean time has not changed, state the probability that the conclusion of the test will be that the population mean time has changed.[1]