Question

4. Weekly sales of regular ground coffee at a supermarket have in the recent past varied according to a normal distribution with mean  = 354 and a standard deviation of  = 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?

a. State the null and alternative hypothesis.

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

c. Calculate the p-value. p = _______________ d. Do you think that there is convincing evidence that sales are higher? ___________ Explain:

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 354
Alternative Hypothesis, Ha: μ > 354

b)

sample mean = 398

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (398 - 354)/(33/sqrt(3))
z = 2.31

c)

P-value Approach
P-value = 0.0104
As P-value < 0.05, reject the null hypothesis.