Question

A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. Houston Charlotte Tucson Akron 45 25 25 10 65 30 30 15 105 35 19 15 55 10 30 10 85 50 10 5 90 70 35 10 x¯i 74.167 36.667 24.833 10.833 s2i 524.167 436.667 82.167 14.167 The competing hypotheses about the mean commute times are ______________ a) H0: μ1 = μ2 = μ3, HA: Not all population means are equal H0: b) Not all population means are equal, HA: μ1 = μ2 = μ3 H0: μ1 = μ2 = μ3 = μ4, HA: c) Not all population means are equal H0: d) Not all population means are equal, HA: μ1 = μ2 = μ3 = μ4

Answer 1

d) H0: Not all population means are equal,

HA: μ1 = μ2 = μ3 = μ4

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

Therefore, for the case above;

Since the underlying hypothesis is that average commute times are different across cities.

Null hypothesis H0: is that Not all population means are equal.

Alternative hypothesis Ha: μ1 = μ2 = μ3 = μ4