Question

The working assumption in the company is that customers spend on average $300 on the company's services. Recently, you started to suspect that things maybe not going to well and that your customers are not spending as much as they did. Set the null and alternative hypotheses that would reflect your concern and then test them at the 5% level of significance using the data in the After_Class_Assignment_Data Excel file.

Observation	Average Annual Spending	Year of First Trsnaction
Customer 1	$392	2014
Customer 2	$57	2015
Customer 3	$297	2013
Customer 4	$329	2014
Customer 5	$361	2016
Customer 6	$258	2016
Customer 7	$351	2016
Customer 8	$367	2010
Customer 9	$197	2017
Customer 10	$450	2013
Customer 11	$94	2017
Customer 12	$105	2017
Customer 13	$68	2010
Customer 14	$293	2017
Customer 15	$75	2012
Customer 16	$172	2010
Customer 17	$75	2010
Customer 18	$290	2011
Customer 19	$282	2011
Customer 20	$434	2010
Customer 21	$277	2013
Customer 22	$142	2010
Customer 23	$366	2015
Customer 24	$464	2012
Customer 25	$216	2013

Answer 1

since,you started to suspect that things maybe not going to well

so, concern is regarding that comapny may spend less than $300 on average.

Ho :   µ =   300
Ha :   µ < 300

sample std dev ,    s =    129.2359
Sample Size ,   n =    25
Sample Mean,    x̅ =   256.480

degree of freedom=   DF=n-1=   24  
          
Standard Error , SE =   s/√n =   25.8472  
          
t-test statistic=   (x̅ - µ )/SE =    -1.684  
          
  
p-Value   =   0.0526 [excel formula =t.inv(-1.68,24) ] ]
Conclusion:     p-value>α=0.05, Do not reject null hypothesis

so, there is no enough evidence that to conlcude that customers spend on average less than $300 on the company's services at α=0.05