Question 847:

1

No answer provided yet.We need to conduct a 2-sample t-test on the difference between independent means here and we're assuming the standard deviations are not equal.

The Null Hypothesis is that there is no difference in the mean waiting times between the two locations. The alternative hypothesis is that the waiting times are different. We will reject the Null Hypothesis if the p-value is less than the alpha cutoff of .05.

The test statistic t* is found as the difference between the sample means divided by the standard error. The difference between means is 1.77 minutes. The standard error of the difference between means (SE) is found by dividing both variances by their sample size, adding them and taking the square root = SQRT [ 19.72/10 + 7.21/12 ] = 1.60.

The test statistics t* is then 1.1047. The degrees of freedom (df) can be found by using 1 less than the smaller of the two sample sizes =10-1=9. The df are used in looking up the p-value.We lookup the p-value using a t-table or the excel function =TDIST(1.1047,9,2) and get the p-value .287 which exceeds the alpha cutoff. Therefore we fail to reject the Null Hypothesis and cannot conclude there is a difference between the mean waiting times.