Exercise 1 Please use Megastar or excel Merrill Lynch regularly asks its custome

Question

Exercise 1 Please use Megastar or excel Merrill Lynch regularly asks its customers assessments of the financial advice and services provided to them. Higher scores indicate better service, with 7 being the highest score. Below are in summarizes the scores given to two financial consultants by members of two independent random samples. A consultant has 10 years of experience, while the consultant B has a year of experience. To Merrill Lynch is interested to know if there is difference between the average populations the scores obtained by each consultant. consultant 1=n1=16 ,x1=6.82,s1=0.64 consultant2= n2=10,x2=6.25,s2=0.75 a) Find the confidence interval two-tailed 99% for the difference between the population means. b) Set the null and alternative hypotheses. c) Calculate the value of the test statistic. d) What conclusion reached? Or not reject the null hypothesis? Use a level significance of 1%. e) There is a relationship between a) and d)? Explain.

Explanation / Answer

Given for consultant 1:      n1=16, x1=6.82, s1=0.64

For consultant 2:   n2=10, x2=6.25, s2=0.75

Null Hypothesis in such types of questions is: H0 There is no difference between the average scores, x1-x2=0

and Alternate Hypothesis is H1 x1-x2 is not equal to zero or x1 is greater than x2

Keeping in view the size of the samples t test is recommended and value of t is calculated as follows:

t = statistic/Standard error =( x1 - x2 ) / SE where SE = sqrt [ (s12/n1) + (s22/n2) ]

t = (6.82-6.25)/sqrt[.642/16)+(.752/10)] = .57/sqrt(.0256+.05625) = .57/.286094 = 1.992349

This calculated value of t is compared with the tabulated value of t at 99% for degree of freedom (n1-1)+(n2-1)=24

Tabulated value is 1.7109. As the calculated value is higher than the tabulated value therefore we have to reject the Null Hypothesis and conclude that the difference between the scores is significant at 1% level of significance.

99 % level of confidence is same as the 1% level of significance meaning we may be wrong in our conclusion in 1% cases.

In case we take alpha one tail 0.025 or two tail alpha as .05 the tabulated value of t is 2.0639 and at that level Null Hypothesis is accepted.

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