Question

You work in a sales department and want to know if a new advertisement campaign is effective at increasing sales. You have three quarters (quarter of a year) of sales data after the new advertisement campaign: Q1= $100,000 , Q2 = $110,000, and Q3= $75,000. You know quarterly sales prior to the new ad campaign followed a normal distribution with a mean of $80,000 and a standard deviation of $10,000. \

-Write the distribution for sales prior to the new advertisement using the notation for a normal distribution: X~

Explain why the sales prior to the new advertisement campaign should be interpreted as the population for this study.

Our null hypothesis is H0: X ̅=80,000. Interpret this hypothesis in words and be sure to identify the population mean in this interpretation.

Calculate the 90% confidence interval for mean quarterly sales following the new advertisement. Conduct a hypothesis test for whether quarterly sales have changed since the new advertisement campaign has been running. Interpret the results of your hypothesis test from part e in words.

Answer 1

(first) the normal distribution is represented as X~N(, ²) so is mean and is standard deviation

X~N(80000, 10000*10000)

(second part) since we are using as reference data ( of   prior to the new advertisement)

(third) the null hypothesis is a general statement or default position and showing no biasness

(fourth)90% confidence interval=(85504,104496)

here =(100,000+110,000+75000)/3=95000 , n=3, =10000

(1-alpha)*100% confidence interval for population mean=sample mean±z(alpha/2)*sd/sqrt(n)

90% confidence interval for population mean=95000±z(0.1/2)*10000/sqrt(3)=95000±1.645*10000/sqrt(3)=95000±9496

	z-value	margin of error	lower limit	upper limit
90% confidence interval	1.645	9496	85504	104496

(fifth) H0:=80000 and alternate hypothesis Ha:80000

here we use z-test and z=(-)/( /sqrt(n))=(95000-80000)/(10000/sqrt(3))=2.598

the critical z(0.1)=1.645 is less than calculated z=2.598, so we reject H0 and conclude that  quarterly sales have changed since the new advertisement campaign