Question

In: Statistics and Probability

Researchers investigating temperament in dogs have a database of reactivity scores from a population of N...

Researchers investigating temperament in dogs have a database of reactivity scores from a population of N = 1000 puppies. The reactivity scores are normally distributed with a mean of mu = 175 and a standard deviation of sigma = 20; higher scores indicate higher reactivity (that is, the puppy is more likely to become aroused by novel stimuli).

Dr. Kobe is also conducting temperament testing, but his local shelter is much smaller than Dr. Santos’. Thus, he is only able to obtain a sample size of n = 20 puppies.

a. What is the likelihood that Dr. Kobe will obtain a mean reactivity score of 168 or lower?

b. What is the likelihood that Dr. Kobe will obtain a mean reactivity score of 190 or higher?

c. Why should the probability of obtaining a sample mean less than M = 165 be larger for Dr. Kobe than Dr. Santos?

Expert Solution

a) P(< 168)

= P(( - )/< (168 - )/(/))

= P(Z < (168 - 175)/(20/))

= P(Z < -1.565)

= 0.0588

b) P(> 190)

= P(( - )/> (190 - )/(/))

= P(Z > (190 - 175)/(20/))

= P(Z > 3.354)

= 1 - P(Z < 3.354)

= 1 - 0.9996

= 0.0004

c) Since the sample size obtained by Dr. Kobe is smaller than Dr. Santos', so the probability of obtaining a sample mean less than 165 will be larger for Dr. Kobe than Dr. Santos'.

orchestra answered 1 year ago

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