Weekly sales of regular ground coffee at a supermarket have in the recent past varied according to a normal distribution with mean  = 354 units per week and standard deviation  = 33 units. The store reduces the price by 5%. Sales in the next three weeks are 405, 378, and 411 units. Is this good evidence that average sales are now higher? The hypotheses are:

H₀:  = 354
H₀:  > 354

Assume that the standard deviation of the population of weekly sales remains  = 33.

a) Find the sample mean x-bar and the value of the one-sample z test statistic.
x-bar =  
z=  

b) Calculate the P-value. (Sketch a standard normal curve and shade the area corresponding to the P-value to help answer this question. Your instructor may wish to see these sketches.)
P-value =  c) Is the result statistically significant at the  = 0.05 level?