Homework 4
Instructions
- Download a printable version of this assignment here. Print it out and record your answers directly in the space provided.
- Write your name and student number on the top of the assignment.
- For problems requiring additional written work, use the allotted work space and/or margins of the page.
- Once you’re done with a problem, reflect on how you well-equipped you felt answering that particular problem using the confidence level assessment shown below.
- Turn in your assignment in class on the due date.
Questions
Question 1
A recent magazine article claimed that “our survey results using a random sample indicate that, on average, American adults watch between 75 and 77 minutes of television per day.”
- What is the population of interest in this example?
_____________________________________ - Based on the reported confidence interval, what is the average amount of time spent watching TV for the sample?
_____________________________________ - What is the margin of error?
_____________________________________ - What other information is needed to assess the quality of the inference made in this statement?
_____________________________________ - Name at least two factors that might help to explain the high precision (i.e., small margin of error) for the confidence interval.
Question 2
A social researcher is interested in estimating the number of friends that college students typically made during their first year of school. Questioning a random sample of 50 students at the end of their freshman year, he finds a mean of 3 friends. Assume that the sample comes from a population with a standard deviation of 1.0.
- Calculate the standard error.
_____________________________________ - Construct a 95% confidence interval to estimate the mean number of friends made by the population of students during their first year on campus.
_____________________________________ - Provide an interpretation of the confidence interval.
Question 3
A school principal is interested in assessing the performance of her students on the Totally Oppressive Standardized test (TOST). She selects a simple random sample of 16 of her students and finds the following set of scores:
6 5 6 12 5 10 11 13
12 10 9 20 23 20 28 18
Assume that the sample is drawn from a population with a standard deviation \(\sigma = 7.20\).
- What is the average score for the sample of students?
_____________________________________ - Calculate the standard error.
_____________________________________ - Find and interpret the 95% confidence interval for the mean.
_____________________________________ - Find and interpret the 99% confidence interval for the mean.
_____________________________________ - Why is the margin of error smaller for the 95% confidence interval in question c than for the 99% confidence interval in question d?
Question 4
A mayor of a big city finds that 212 of 400 randomly selected city residents believe that that believes that the city should spend more money on road maintenance. Use this information for a large-sample inference of the proportion of all city residents who believe that the city should be spending more.
- What percentage of the sample members believe the city should be spending more?
_____________________________________ - Calculate the standard error of the proportion.
_____________________________________ - Find and interpret the 95% confidence interval for the population proportion.
_____________________________________ - Based on your findings, is it safe to say that a majority of the city’s population wants more spent on roads? Explain your answer.