As a result of dog breeding for certain physical traits, many dog breeds have changed in the last 100 years. One example is basset hounds, whose height has decreased as a result of breeding. Suppose that researchers compare measurements from a random sample of 36 male basset hounds taken in 1915 and a random sample of 36 male basset hounds taken in 2015. Suppose the difference in mean heights (2015 basset hounds minus 1915 basset hounds) is –2.8 cm and the 90% confidence margin of error is 1.3 cm. The 90% confidence interval is –4.1cm to –1.5cm.

What is best conclusion about the change in height of basset hounds?

Using a sample of 36 male basset hounds taken in 1915 and a sample of 36 male basset hounds taken in 2015 a 90% CI for the difference of mean weights of the basset hounds (2015-1915) was constructed:

Group 1

X₁: Weight of a basset hound measured in 1915

n₁= 36

Group 2

X₂: Weight of a basset hound measured in 2015

n₂= 36

Difference X₂ - X₁

X[bar]₂ - X[bar]₁= -2.8cm

margin of error d= 1.3cm

90% CI: [-1.4; -1.5]cm

The calculated CI is two-tailed, you can use it to decide over a two-tailed hypothesis test for the same parameter of interest over the same level. If the hypothesis is:

H₀: μ₂ - μ₁=0

H₁: μ₂ - μ₁≠0

α: 0.10

The CI doesn't contain the zero, so you could reject the null hypothesis. With this, you can conclude that the difference between the average weight of the basset hounds in 2015 and the average weight of the basset hounds in 1915.

Judging by the fact that both limits of the confidence interval are negative, as well as the difference between point estimators, it seems that the weight of the basset hounds in 2015 is less than their weight in 1915. Of course, you are not valid to make that kind of conclusion without a proper hypothesis test.