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 = 0.64consultant b: n = 10, x = 6.25, s = 0.75a. 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?

a) Null hypothesis:

Alternative hypothesis:

b)  

c)

d) If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, and the more experience consultant A have a significant higher rate compared to the consultant B with less experience at 5% of significance.

Step-by-step explanation:

1) Data given and notation

represent the mean for the sample of Consultant A

represent the mean for the sample of Consultant B

represent the sample standard deviation for the sample of Consultant A

represent the sample standard deviation for the sample of bonsultant B

sample size selected for the Consultant A

sample size selected for the Consultant B

represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

represent the p value for the test (variable of interest)

Part a: State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the Consultant A (more experience) is higher than the mean for the Consultant B, the system of hypothesis would be:

Null hypothesis:

Alternative hypothesis:

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

(1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Part b: Calculate the statistic

We can replace in formula (1) the info given like this:

Part c: P-value

The first step is calculate the degrees of freedom, on this case:

Since is a one side test the p value would be:

Part d: Conclusion

If we compare the p value and the significance level given we see that so we can conclude that we have enough evidence to reject the null hypothesis, and the more experience consultant A have a significant higher rate compared to the consultant B with less experience at 5% of significance.