Question

A researcher wished to compare the average daily hotel room rates between San Francisco and Los Angeles. The researcher obtained an SRS of 15 hotels in downtown San Francisco and found the sample mean x1=$156 , with a standard deviation s1= $15 . The researcher also obtained an independent SRS of 10 hotels in downtown Los Angeles and found the sample mean x2= $143, with a standard deviation s2=$10.
Let 1 and 2 represent the mean cost of the populations of all hotels in these cities, respectively. Assume the two-sample t procedures are safe to use, i.e. Unequal Variances.

1.Suppose the researcher had wished to test the hypotheses H0 : µ1 = µ2 vs. Ha : µ1 ≠ µ2 at the
5% significance level (i.e., α = 0.05). The numerical value of the two-sample t statistic is?

2. P value?

3.What are your statistical conclusion and its interpretation? Use significance level, α = 0.05 (or 5%).

4.Based on your P-value and conclusion in (b) and (c), will you conclude that a 99% confidence
interval for µ1 - µ2 includes the value 0? Explain.

Answer 1

1)

2)

df= 22.993~23

p value = 2*p(t>2.6) = 0.016

c)

d)

Since null hypothesis is rejected so we can say that confidence interval for µ1 - µ2 does not contain 0.