Question

1)

Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services on a 7-point scale (7 is the maximum). You are a manager with two consultants you are trying to compare. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. You want to test if the consultant with less experience has a rating that is different than the more experienced consultant. So, you collect independent samples of service ratings for these two financial consultants. Consultant A has 11 surveys with a mean of 6.66 and standard deviation of 0.63. Consultant B has 18 surveys with a mean of 6.43 and standard deviation of 0.58. You wish to test the claim at a significance level of α=0.05α=0.05.

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample?
   
   p-value =  Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the consultant with less experience (B) has a rating that is different than the more experienced consultant (A).
   • There is not sufficient evidence to warrant rejection of the claim that the consultant with less experience (B) has a rating that is different than the more experienced consultant (A).
   • The sample data support the claim that the consultant with less experience (B) has a rating that is different than the more experienced consultant (A).
   • There is not sufficient sample evidence to support the claim that the consultant with less experience (B) has a rating that is different than the more experienced consultant (A).

2)

A market research firm used a sample of individuals to rate the purchase potential of a particular product before and after the individuals saw a new, expensive television commercial about the product. The purchase potential ratings were based on a 0 to 10 scale, with higher values indicating more potential to purchase the product. You want to know if the commercial increased the mean purchase potential rating. You will test the claim at a significance level of  αα = 0.005. To do so, you find a sample of 36 people, you find the mean "after-before" rating to be ¯d=0.4d¯=0.4 with a standard deviation of the differences of sd=sd= 0.8.  

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample? Round to 4 decimal places.
   
   p-value =
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the mean 'after'-'before' rating is greater than 0.
   • There is not sufficient evidence to warrant rejection of the claim that the mean 'after'-'before' rating is greater than 0.
   • The sample data support the claim that the mean 'after'-'before' rating is greater than 0.
   • There is not sufficient sample evidence to support the claim that the mean 'after'-'before' rating is greater than 0.

Answer 1

Solution-1:

Ho:mu1=mu2

Ha:mu1 not = mu2

mu1 for mean for less experience

and mu2 mean for more experience

alpha=0.05

in Ti83 cal

STAT>2-SampTTest

we get

t=-0.9828

p=0.3375

p>alpha

Fail to reject null hypothesis.

There is not sufficient sample evidence to support the claim that the consultant with less experience (B) has a rating that is different than the more experienced consultant (A).

Solution-2:

t=dbar/sd/sqrt(n)

=(0.4)/(0.8/sqrt(36)

t=3.0000

p=0.0025

p<alpha

p value is less than alpha

reject null hypothesis

There is sufficient evidence to warrant rejection of the claim that the mean 'after'-'before' rating is greater than 0.