The average height and weight of women varies around the world, but in the United States
in 2010, the average adult female height was 63.8 inches (approximately 5 feet 4 inches) and
166.2 pounds, according to the Centers for Disease Control and Prevention. It is believed that
women from the Midwest are taller as compared to other regions. We want to test this claim
and we use the Getting To Know You Survey data to support the claim that average
height of Minnesotan women enrolled in University of Minnesota is greater than 63.8 inches?
Test at α = 0.05.
(a) State the parameter of interest.
(b) Give assumptions for the statistical test. Discuss if the assumptions will be met for the
problem.
(c) State H0 and H
(a) height
(b) U of M women is biased sample of Minnesota women.
(c) Ho: U of M height = US height
Ha: U of M height ≠ US height
(a) The parameter of interest is the average height of Minnesotan women enrolled in the University of Minnesota.
(b) The assumptions for the statistical test are as follows:
1. The sample is randomly selected from the population.
2. The height data are normally distributed.
3. The variances of height in the population and the sample are equal.
The first assumption can be met if the sample is selected randomly from the population of Minnesotan women enrolled at the University of Minnesota.
The second assumption can be checked by examining the distribution of the height data. If the data follows a roughly bell-shaped curve, then this assumption would be considered reasonable.
The third assumption can be difficult to confirm without additional information. We would need knowledge of the population variance or use statistical tests to compare variances. However, if the sample size is large enough (typically taken to be 30 or greater), the assumption of equal variances is often not critical.
(c) The null hypothesis (H0) is that the average height of Minnesotan women enrolled in the University of Minnesota is equal to or less than 63.8 inches.
The alternate hypothesis (Ha) is that the average height of Minnesotan women enrolled in the University of Minnesota is greater than 63.8 inches.
H0: μ ≤ 63.8
Ha: μ > 63.8
Note that we are testing if the average height is greater, therefore the alternative hypothesis is one-tailed.