Question

An investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. The investigator gets a sample of 21 country owners. The mean number of hours per week that city owners (known population) spend walking their dogs is 10.0. The mean number of hours country owners spent walking their dogs per week was 15.0. The standard deviation of the number of hours spent walking the dog by owners in the country was 4.0. Do dog owners in the country spend more time walking their dogs than do dog owners in the city? Please test the investigator's theory using an alpha level of .05.

For each of the single sample t-tests below (problem 1-3), please include:
1) The null and alternative hypotheses (can be written in notation or as a sentence)
2) Calculate (show all work):
a) The estimated population variance
b) The variance of the distribution of means
c) The standard deviation of the distribution of means
3) Degrees of freedom
4) The cutoff sample score on the comparison distribution at which the null hypothesis
should be rejected (cutoff scores)
5) The sample’s score on the comparison distribution (e.g. t-obtained) (show all work)
6) Decide whether to reject the null hypothesis
7) State your conclusion in APA format (make sure to report what groups you are comparing
(and their means), what the DV is, whether it was significant or not and your test statistic (t)
(see the lecture slides for examples).

Answer 1

(1)

H0: Null Hypothesis: ( dog owners in the country do not spend more time walking their dogs than do dog owners in the city)

HA: Alternative Hypothesis: ( dog owners in the country spend more time walking their dogs than do dog owners in the city) (Claim)

(2)

(a)

The estimated population variance = 4² = 16

(b)

The variance of the distribution of means is given by:

(c)

The standard deviation of the distribution of means is given by:

(3)

Degrees of freedom = 21 - 1 = 20

(4)

The cutoff sample score on the comparison distribution at which the null hypothesis
should be rejected (cutoff scores) :

1.725

(5)

The sample’s score on the comparison distribution (e.g. t-obtained) is got as follows:

(6)

Since calculated value of t = 5.728 is greater than critical value of t = 1.725, the difference is significant. reject null hypothesis.

Conclusion:
The data support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city.

(7)

The research question is: Do dog owners in the country spend more time walking their dogs than do dog owners in the city.?. For this Hypothesis Test, One Sample t test is used. For Degrees of Freedom = n - 1 = 21 and Significant Level = =0.05, the critical value of t = 1.725. From the given data, t value was got as t_obtained = 5.728. Since calculated value of t = 5.728 is greater than critical value of t = 1.725, the difference is significant. reject null hypothesis. The the conclusion arrived at was: The data support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city.