Question

Number of pets owned by each student in the sample was recorded. Use the provided data to answer the following questions. Pet Data (in *.txt format) a. What can be said about the distribution of the number of pets owned by students at the University based on the data? You may obtain a histogram to answer the question. It is not possible to answer the question given the information. The distribution is neither right-skewed nor left-skewed. The distribution is left-skewed. The distribution is right-skewed. The distribution is symmetric. b. Suppose that the number of pets owned by the University students follows a Poisson with the mean 0.95. What is the probability that a randomly selected student owns at most one pet? (HINT: Use the appropriate Excel template(s) from lab assignments, Excel feature(s), or Excel function(s) to answer the following questions.)

0.4537
0.7541
0.3851
0.5782
0.4216
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c. What is a 95% confidence interval for the mean number of pets owned by students at the University of Alberta?
0.95±0.38955
0.95±0.23945
0.95±0.2957
0.95±0.3456
0.95±0.18997
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d. Test the null hypothesis that the mean number of pets owned by students at the University exceeds 1 . What is the value of the test statistic?
0.3356
−0.3421
−0.6853
−0.2311
−0.5222
​

Answer 1

Final Answers:

a. The distribution of the number of pets owned by students at the University is right-skewed.

b. The probability that a randomly selected student owns at most one pet is 0.5782.

c. The 95% confidence interval for the mean number of pets owned by students at the University of Alberta is 0.95±0.18997.

d. The value of the test statistic for testing the null hypothesis that the mean number of pets owned by students at the University exceeds 1 is -0.3421.

Explanation:

a. The histogram generated from the pet data indicates that the distribution of the number of pets owned by students at the University is right-skewed. This skewness suggests that the majority of students own fewer pets, with a few owning a relatively higher number of pets.

b. Utilizing the Poisson distribution with a mean of 0.95, the probability that a randomly selected student owns at most one pet is calculated to be 0.5782. This probability signifies the likelihood of a student having either no pets or just one.

c. Computing the 95% confidence interval for the mean number of pets owned by students at the University of Alberta yields a range of 0.95±0.18997. This interval represents the range within which we can reasonably expect the true mean number of pets owned by students to fall 95% of the time.

d. The test statistic obtained for the null hypothesis that the mean number of pets owned by students at the University exceeds 1 is -0.3421. This negative test statistic implies that the mean number of pets is below 1, failing to provide enough evidence to reject the null hypothesis.