Question

In: Statistics and Probability

A researcher is curious if age makes a difference in whether or not students make use...

A researcher is curious if age makes a difference in whether or not students make use of the gym at a university. He takes a random sample of 30 days and counts the number of upperclassmen (Group 1) and underclassmen (Group 2) that use the gym each day. The data are below. The population standard deviation for underclassmen is known to be 22.57 and the population standard deviation for upperclassmen is known to be 13.57.

Upper Classmen average = 202.4, population SD = 13.57, n = 30

Under Classmen average = 191.3, population SD = 22.57, n = 30

Is there evidence to suggest that a difference exists in gym usage based on age? Construct a confidence interval for the data above to decide. Use α=0.10. Confidence Interval (round to 4 decimal places):

_____ < μ1 - μ2 < _____

Solutions

Expert Solution

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(184.1449/30 + 509.4049/30)
sp = 4.8082

Given CI level is 0.9, hence α = 1 - 0.9 = 0.1                  
α/2 = 0.1/2 = 0.05, zc = z(α/2, df) = 1.645                  
                  
Margin of Error                  
ME = zc * sp                  
ME = 1.645 * 4.8082                  
ME = 7.909                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (202.4 - 191.3 - 1.645 * 4.8082 , 202.4 - 191.3 - 1.645 * 4.8082                  
CI = (3.1905 , 19.0095)                  
                  
                  

orchestra answered 1 year ago
Next > < Previous

Related Solutions

A researcher is curious if age makes a difference in whether or not students make use...
A researcher is curious if age makes a difference in whether or not students make use of the gym at a university. He takes a random sample of 30 days and counts the number of upperclassmen (Group 1) and underclassmen (Group 2) that use the gym each day. The data are below. The population standard deviation for underclassmen is known to be 22.57 and the population standard deviation for upperclassmen is known to be 13.57. Upper Classmen average = 202.4,...
A researcher wants to determine whether there is a difference in the average age of elementary...
A researcher wants to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Can you reject the claim that there is no difference in the average age of each group? Use 5% level of significance. Elementary Teachers High School Teachers CC Teachers 24 37 45 28 42 36 25 39 39 52 48 61 36 43 35 22 32 45 a)...
A researcher was curious about whether people’s attitudes are related to their behaviors. As a simple...
A researcher was curious about whether people’s attitudes are related to their behaviors. As a simple experiment, the researcher measured people’s attitudes and behaviors regarding housework. On the attitude side, the researcher measured the level of agreement on the statement “It is much better for everyone involved in housework: strongly agree, agree, disagree, and strongly disagree” On the behavioral side, the respondents are asked to estimate how many hours of housework they do per week. Based on your analysis of...
A professor was curious as to whether the students in a very large class she was...
A professor was curious as to whether the students in a very large class she was teaching, who turned in their tests first, scored differently from the class mean on the test. The μ on the test was 75 with σ = 10; the scores were approximately normally distributed. The mean score for the first 20 tests was 78. Did the students turning in their tests first score significantly different from the larger mean at the .05 level? a) Use...
A nursing professor was curious as to whether the students in a very large class she...
A nursing professor was curious as to whether the students in a very large class she was teaching who turned in their tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 tests was 78. Did the students turning in their tests first score significantly different from the mean?
3. A nursing professor was curious as to whether the students in a very large class...
3. A nursing professor was curious as to whether the students in a very large class she was teaching who turned in their tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 tests was 78. Did the students turning in their tests first score significantly different from the mean? Explain....
A researcher wants to assess if there is a difference in the average age of onset...
A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let = average age of onset for women and = average age of onset for men. A random sample of n1 = 30 women with the disease showed an average age of onset of = 83 years, with a sample standard deviation of s1 = 11.5 years. A random sample of n2...
A researcher wanted to know if there is an age difference in the amount of time...
A researcher wanted to know if there is an age difference in the amount of time spent on social media. They collected data from 8 teenagers (13-18 years old) and 8 young adults (21-26 years old); they measured the average number of hours spent using all social media platforms over the course of a day. The mean hours spent on social media for teenage participants was 2.9750 with a variance of 1.0630 and the mean hours spent on social media...
A) Suppose that a medical researcher wants to explore whether there is an effect of age...
A) Suppose that a medical researcher wants to explore whether there is an effect of age in systolic blood pressure for males between 40 to 60 years old. To investigate the relationship, a random sample of 100 males between 40 to 60 years old were selected and their systolic blood pressure was recorded. Identify each of the following for this experiment. Subjects: Individuals between 40 to 60 years old Or Males between 40 to 60 years old Or Systolic blood...
A researcher is interested in whether or not there is a difference in student’s performance based...
A researcher is interested in whether or not there is a difference in student’s performance based on the study methods they use. Participants are assigned one of three different study methods (read the text and re-read it, read and answer prepared questions, and read then create your own questions). There are 6 people in each group and the researcher measures the participants’ performance on a test. Perform a hypothesis test and show all four steps. Hints: Use a two tailed...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT