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akkira02
akkira02
15.05.2021 • 
Mathematics

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. (Reference: Elegans, C. 100 Years of Breed Improvement. 2012. Dog Behavior Science. Retrieved from: https://dogbehaviorscience.wordpress.com/2012/09/29/100-years-of-breed-improvement (Links to an external site.))

Which of the following is a valid conclusion about the change in height in basset hounds?

We are 90% confident that our sample of basset hounds from 1915 and 2015 will have a difference in sample means between –1.5 cm to –4.1cm.
We are 90% confident that there is no difference in mean heights between 1915 and 2015. The negative values suggest that the –2.8 sample difference is not statistically significant.
Incorrect. “We are 90% confident that there is no difference in mean heights between 1915 and 2015. The negative values suggest that the –2.8 sample difference is not statistically significant” is not a valid conclusion. The interval does not contain zero. The negative differences suggest that
We are 90% confident that basset hounds in 1915 were 1.5cm shorter on average and in 2015 are 4.1cm shorter on average.
We are 90% confident that the 2015 basset hounds are between 4.1 cm to 1.5 cm shorter on average than the 1915 basset hounds.

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