A food company is developing a new breakfast drink and their

A food company is developing a new breakfast drink, and their market analysts are currently working on preliminary taste-testing studies. To help with their marketing strategy, they were first interested in whether preference for the new product was related to a person\'s gender. There were 100 male and 100 female volunteers available for the taste test. Both the males and females tasted the product and rated the flavour on a scale of 1 to 10, 1 being “very unpleasant” and 10 being “very pleasant.” The mean rating for males was 1 x = 6.4, with a standard deviation s1 = 1.5. The mean rating for females was 2 x = 7.0, with a standard deviation s2 = 2.0. Let µ1 and µ2 represent the mean ratings we would observe for the populations of males and females, respectively, and assume our samples can be regarded as samples from these populations.

1 Suppose the researcher had wished to test the hypotheses Ho:u1=u2 Ha: u1u2

The numerical value of the two-sample t statistic is:

2. If we had used the more accurate software approximation to the degrees of freedom, we would have used which of the following for the number of degrees of freedom for the tprocedures?

Solution

Sample N Mean StDev SE Mean
1 100 6.40 1.50 0.15
2 100 7.00 2.00 0.20

Difference = mu (1) - mu (2)
Estimate for difference: -0.600
95% CI for difference: (-1.093, -0.107)
T-Test of difference = 0 (vs not =): T-Value = -2.40 P-Value = 0.017 DF = 198
Both use Pooled StDev = 1.7678