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?

Solutions

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

Next > < Previous

Related Solutions

Researchers developed a "dog IQ test" and find that the population of dogs in the United...

Researchers developed a "dog IQ test" and find that the population of dogs in the United States has a mean score of µ = 20 on this test with a standard deviation of σ = 2. You decide to test a sample of n = 40 dogs to do some research about whether some breeds are smarter. Use that information to answer all of the following questions: A. What is the expected value of the sampling distribution of the mean?...

A random sample of n = 100 scores is selected from a normal population with a...

A random sample of n = 100 scores is selected from a normal population with a mean of μ = 60 and a standard deviation of σ = 20. What is the probability of obtaining a sample mean greater than M = 57?

A sample of n = 16 scores is obtained from a population with µ = 50...

A sample of n = 16 scores is obtained from a population with µ = 50 and σ = 16. If the sample mean is M = 58, then what is the z-score for the sample mean? z = - 2.00 z = +0.50 z = +2.00 z = +8.00 A researcher selects a random score from a normally distributed population. What is the probability that the score will be greater than z = +1.5 and less than z =...

If two random samples, each with n = 60 scores, are selected from a population, and...

If two random samples, each with n = 60 scores, are selected from a population, and the z-score and t statistic are computed for each sample, the t statistics will be less variable than the z-scores.

6.A sample of n = 16 scores is obtained from a population with µ = 50...

6.A sample of n = 16 scores is obtained from a population with µ = 50 and σ = 16. If the sample mean is M = 58, then what is the z-score for the sample mean? z = - 2.00 z = +0.50 z = +2.00 z = +8.00 7.A researcher selects a random score from a normally distributed population. What is the probability that the score will be greater than z = +1.5 and less than z =...

A sample of n=25 scores is selected from a normal population with μ = 100 and...

A sample of n=25 scores is selected from a normal population with μ = 100 and σ = 20 . a. What is the probability that the sample mean will be greater than 120? b. What is the probability that the sample mean will be less than 105? c. What is the p (90 < M < 110)?

A sample of n = 9 scores is obtained from a normal population distribution with σ...

A sample of n = 9 scores is obtained from a normal population distribution with σ = 12. The sample mean is M = 60. a. With a two-tailed test and α = .05, use the sample data to test the hypothesis that the population mean is μ = 65. b. With a two-tailed test and α = .05, use the sample data to test the hypothesis that the population mean is μ = 55. c. In parts (a) and...

A population of scores with a μ = 43 a n d σ = 8 is...

A population of scores with a μ = 43 a n d σ = 8 is standardized to create a new population distribution with a μ = 50 a n d σ = 10 . What is the new X value for each of the following scores from the original population? a. X = 43 b. X = 47 c. X = 55 d. X = 35

1) Researchers have found that providing therapy dogs on college campuses near midterms and finals is...

1) Researchers have found that providing therapy dogs on college campuses near midterms and finals is an effective way to reduce student stress. They wondered if providing other animals would also reduce stress. To find out, they brought four different animals to campus and had students rate their stress level after time spent with the animal. The results are presented below. OBSERVED Dog Cat Ferret Lizard More Stressed 18 32 38 92 Same Stressed 30 28 42 40 Less Stressed...

Researchers investigating characteristics of gifted children collected data from schools in a large city on a...

Researchers investigating characteristics of gifted children collected data from schools in a large city on a random sample of thirty-six children who were identified as gifted children soon after they reached the age of four. The following histogram shows the distribution of the ages (in months) at which these children first counted to 10 successfully. Also provided are some sample statistics. USE THE TI CALCULATOR (Z-TEST and Z-INTERVAL) for the needed values. n 36 min 21 mean 30.69 sd 4.31...

Subjects