Periodically, merrill lynch customers are asked to evaluate merrill lynch financial consultants and services. higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. independent samples of service ratings for two financial consultants are summarized here. consultant a has 10 years of experience, whereas consultant b has 1 year of experience. use α= .05 and test to see whether the consultant with more experience has the higher population mean service rating.

consultant a: n = 16, x = 6.82, s = 0.64
consultant b: n = 10, x = 6.25, s = 0.75

a. state the null and alternative hypotheses.
b. compute the value of the test statistic.
c. what is the p-value?
d. what is your conclusion?

See the explanation

Step-by-step explanation:

(a)  

H0: Consultant with more experience has the higher population mean service rating.

H1: Consultant with more experience doesn't have the higher population mean service rating.

(b)  

t = 1.9923 (see the attached image)

(c)

The degrees of freedom for the test statistic,

df = 16

The P-value of the one tailed t- test with 16 degrees of freedom is,

P−value = tdist(X,df,tails)

P-value = tdist(1.9923,16,1)

P-value = 0.032

(d)

Since, P-value 0.032 is less than the significance level 0.05, there is an enough evidence to reject the null hypothesis.

Hence, there is a sufficient evidence to conclude that Consultant with more experience doesn't have the higher population mean service rating.

Hope this helps!

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this