In: Statistics and Probability
A large furniture store has begun a new ad campaign on local television. Before the campaign, the long term average daily sales were $24.819. A random sample of 40 days during the new ad campaign gave a sample mean daily sale average of x = $25.630. Does this indicate that the population mean daily sales is now more than $24.819? Use a 1% level of significance. Assume o = $1,917.
a. What is the LEVEL of SIGNIFICANCE? State the NULL
and ALTERNATE HYPOTHESES. Will you use a LEFT-TAILED, RIGHT-TAILED,
or TWO-TAILED test?
b. Identify the sampling distribution you will use: THE STANDARD
NORMAL or THE STUDENT'S t DISTRIBUTION. What is the value of the
SAMPLE TEST STATISTIC?
c. Find (or estimate) the P VALUE or P VALUE RANGE. Sketch the
sampling distribution and SHOW THE AREA CORRESPONDING TO THE P
VALUE. (Alternate method: find the critical value (s) and sketch
the CRITICAL REGIONS and the sample test statistic on the normal
curve.
d. Based on your answer, will you REJECT or FAIL TO REJECT THE NULL
HYPOTHESIS?
e. INTERPRET your decision in the context of the application.