We are interested in studying the relationship satisfaction of young adults before and after they go off to college and are separated from their significant other. A random sample of 35 young adults who are about to be separated from their significant other by going to college was collected. Each participant was asked a series of questions, which was then converted to asatisfaction scoreranging from 0-50 points (a higher score indicates greater satisfaction). The satisfaction score for each participant was measured before leaving for college and after spending the first semester at college away from their significant other. For each participant, the difference in satisfaction score was computed (satisfaction score after minus satisfaction score before).The90% confidence interval for the population mean difference in satisfaction scorefor all such young adults who are separated from their significant other after one semester of college is given by: -9.0points to -0.9points.

Question 1 Subquestions1.a 2 point(s)

Based on the provided 90% confidence interval, do the data support that the population mean satisfaction scoresignificantlychangedafter going off to collegefor the population of all such young adults (at the 10% significance level)? State your answer ofYesorNoand provide a brief explanationin context.

Student answer No answer entered. 1.b 0 point(s)

Is the following statementTrue or False?About 90% of all such young adults who separate from their significant other to attend college will have a decrease in satisfaction score between 0.9 and 9.0 points.

• True
• False

1.c 0.5 point(s)

Is the following statementTrue or False?If this study were repeated many times, with random samples of 35 young adults who separate from their significant other, and for each sample a corresponding 90% confidence interval was made, 90% of the resulting intervals are expected to contain the sample mean difference in satisfaction score.

• True
• False

1.d 0 point(s)

Is the following statementTrue or False?The Central Limit Theorem states that since the sample is large enough (larger than 25 or 30), then we can conclude that the difference in satisfaction scores (difference = After - Before) for the population of all such young adults follows approximately a normal distribution.

• True
• False

1 point(s) Question 2 :

Confidence Level for population mean difference in time

A professor wanted to know if the amount of time his students spent on Facebook exceeded the time they spent studying, on average. From one of his large lectures of 200 students, he took a random sample of 20 students and asked them to report the number of hours they spent on Facebook in a week and the number of hours they spent studying in that same week. He computes a 90% confidence interval for the population mean difference (difference computed as Facebook time - studying time). His resulting confidence interval is (-5.2, -0.3). The 90% confidencelevelis: (select all that are correct)

Question 2 Multiple Choice Options

• the probability the procedure will provide a 90% confidence interval that covers the sample mean difference in time (Facebook time - studying time), if the study were repeated in the future.
• the probability of making a Type 1 error if the 90% confidence interval is used to test the null hypothesis that the population mean difference in time (Facebook time - studying time) is zero.
• the probability that students in the population will have a difference in time (Facebook time - studying time) that falls in the 90% confidence interval.
• the probability the procedure will provide a 90% confidence interval that covers the population mean difference in time (Facebook time - studying time), if the study were repeated in the future.
• None of the above are correct.

Question 3 Background :

Measuring E. coli Levels

Agricultural researchers wish to compare two methods for measuring the level ofE. colibacteria contamination in beef. Two different methods (A and B) were used on each of ten randomly selected specimens of a certain type of beef. Theresulting measurements (in milimicrobes/liter)can be found in the data setEColi.RData.

Question 3 Subquestions3.a 2 point(s)

You have been asked to analyze the data. In particular, you are asked toestimate the population mean difference inE. colilevel. UseR (R Commander) to computea new variabledifference= MethodB MethodA. Then use R to compute those summary statistics for the differences. Be sure to include the mean, standard deviation, IQR, five number summary,and thestandard error of the mean. Copy and paste inthose descriptive statistics from the R output in your text answer box.Below the R output, provide the sample mean difference inE. colilevel and the standard error of the mean, including units.

Student answer No answer entered. 3.b 0 point(s)

Use R (R commander) to provide a 95% confidence interval estimate for thepopulation mean difference inE. colimeasurements (where difference =Method B - Method A). Copy and paste in R output in your text answer box. Below the R output, provide the 95% confidence intervalincluding units.

Student answer No answer entered. 3.c 0.5 point(s)

Based on theconfidence interval, do the two methods appear to be significantly different (at the 5% level) in terms of measuringE. coli,on average?

• Yes, since the interval is quite narrower and does not contain very many reasonable values.
• No, since 95% confidence interval does contain the value of zero.

1 point(s) Question 4 :

What does it mean?

You interview 100 University of Michigan students in their freshman year and again in their senior year and ask each about the typical number of minutes per day that they spend using social media. Let_drepresent the population mean difference in timespent using social media (freshman - senior).You wish to testthe hypotheses H₀:_d= 0 versusH_a:_d0. You compute the 95% confidence interval for_dand find it to be (13.2 minutes, 24.8 minutes). Assume the necessary conditions for conducting the confidence interval and test are met. Which of the following are correctstatements? Select all that are correct.

Question 4 Multiple Choice Options

• You would reject the null hypothesis at the 5% level.
• Your would fail to reject the null hypothesis at the 5% level.
• The p-value for the test is more than 0.05.
• A mistake has been made as the confidence interval should contain 0 about 95% of the time.

1 point(s) Question 5 :

Statistical Significance

Which of the following statements about statistical significance is (are) correct? Select all that are correct.

Question 5 Multiple Choice Options

• If a result is statistically significant at the 5% level, it is also significant at the 1% level.
• If a result is statistically significant at the 5% level, it is also significant at the 10% level.
• If we select a 5% level, we are requiring that the data provide evidence against the null hypothesis so strong that seeing data that strong or stronger would happen no more than 5% of the time when the null hypothesis is true.
• If the null hypothesis is true, then the significance level is also the probability of rejecting the null hypothesis.
• The significance level is the probability that the null hypothesis is true.

Question 6 Background :

Was it Colder?

A meteorologist wants to determine if it was colder this past October than it was in October of the previous year, on average, using a10% significance level. From each October month, he randomly selects 8 different days from each year and records the temperature. Let Group 1 = temperatures from October this past year and Group 2 = temperatures from October the previousyear.

Question 6 Subquestions6.a 2 point(s)

Which of the following is the appropriate symbol to complete set of hypotheses?

H₀:₁=₂versusH_a:₁?₂

• > (greater than or one-sided to the right)
• < (less than or one-sided to the left)
• not equal to (two-sided)

6.b 0 point(s)

Suppose the meteorologist conducts the appropriate test and obtains ap-value of 0.076 and thus decides to reject the null hypothesis. What type of error could he have made?

• Type 1 error
• Type 2 error
• Since the decision has been made, no error is possible.

1 point(s) Question 7 :

Paired t-Test Assumptions

To use a paired t confidence interval to estimate the population mean difference in responses, or to perform a paired t test regarding hypotheses about the population mean difference, there are some assumptions (or conditions). Which of the following is a (are) required assumption(s)? Select all that apply.

Question 7 Multiple Choice Options

• The two sets of measurements that are used to form the pairs are independent random samples.
• The number of paired observations (or differences) is more than 30.
• The distribution of the population of all differences in responses is normal.
• The standard deviation for the population of all differences is known.

Question 8 Background :

Cell Phones and Driving

An experiment was designed to assess whether the use of cell phones during driving generally increases a drivers reaction time. A random sample of 32 students was selected for the study. Each student was tested twice for reaction time in a simulated driving experience, oncewithoutan ongoing cell phone conversation and oncewithan ongoing cell phone conversation. Half of the students were randomly selected to have a reaction time assessment within the first three minuteswithouta cell phone conversation followed by a reaction time assessment again in the next three minuteswitha cell phone conversation. For the other half, the order of the two conditions (withoutversuswith) was reversed.

Many factors were carefully controlled for during the experiment. For example, theinstructions given to each studentwere the same, during thewith cell phoneassessmentthe length of conversation with the caller andthe script for the conversationwas the same.Thereaction timewas measured as the time between a trafficlight turningred and the student engaging the brake (to the nearestmillisecond).The resulting data are given in the data set namedCellPhone.Rdata.

Question 8 Subquestions8.a 2 point(s)

The researchers wished to assess if the reaction time would increase with the use of a cell phone on average for the population of all student drivers. Let the parameter_drepresent the population meandifference in reaction time (withoutcelllesswithcell) for the population of all student drivers. The researcher knows that the null hypothesis of no difference on average should be expressed asH₀: _d= 0. Which direction is the appropriate one to correctly complete the alternative hypothesisH_a: _d __ 0?

• greater than (>)
• less than (<)
• not equal to

8.b 0 point(s)

Generate theR paired samples t test output.Copy and paste the test results from R Commanderin for your answer.

Below the results state the test statistic value and the corresponding p-value.

Test statistic t = _________ and p-value = __________

Student answer No answer entered. 8.c 0.5 point(s)

Here are some additional summary measures of the differences in reaction times.

> numSummary(CellPhone[,"difference"], statistics=c("mean", "sd", "se(mean)", + "IQR", "quantiles"), quantiles=c(0,.25,.5,.75,1)) mean sd se(mean) IQR 0% 25% 50% 75% 100% n -50.625 52.48579 9.278264 75.25 -150 -84.75 35.5 -9.5 24 32

Which of the following (slightly rounded)valuesfrom this summaryoutput correctly completes this interpretation statement?

We would estimate the possible sample mean differences in reaction time (values) to be about ______ milliseconds away from the population mean difference in reaction times _d, on average.

• -50.6
• 52.5
• 9.3

8.d 0 point(s)

What distribution is used to find thep-value for the test?

• standard normal N(0,1) distribution
• a t(31) distribution
• a t(32) distribution

8.e 0 point(s)

Based on the test results, what decision and conclusion should be made at a 10% significance level? Select one:

• Reject the null hypothesis and conclude there is insufficient evidence to demonstrate that the use of a cell phone increases reaction time on average for the population of student drivers represented by this sample.
• Reject the null hypothesis and conclude there is sufficient evidence to demonstrate that the use of a cell phone increases reaction time on average for the population of student drivers represented by this sample.
• Fail to reject the null hypothesis and conclude there is insufficient evidence to demonstrate that the use of a cell phone increases reaction time on average for the population of student drivers represented by this sample.
• Fail to reject the null hypothesis and conclude there is sufficient evidence to demonstrate that the use of a cell phone increases reaction time on average for the population of student drivers represented by this sample.

8.f 0 point(s)

Someone on the research team wondered if the study could have been conducted as two independent samples (with 32 subjects per condition). The director of the study responded such a study was possible, but that by using each patient as his own control in their study, they had reduced the variability of the response (and, hence, reduced the necessary sample size).

The research team member alsoremembered that one assumption for this test to be valid is that the differences in reaction times can be considered a random sample from the population of interest. The provided graph was made for checkinganotherrequired assumption to conduct the hypothesis test.

Clearlystatethe assumption that this graph helps to assess (in context).

Student answer No answer entered.

Question 9 Background :

Inter-Rater Reliability

Two different technicians (Tech A and Tech B) each measured the cardiac output for a sample of 36 patients using Doppler Echocardiaography. The supervisor would like to use this paired data to assess inter-rater reliability by testing if the population mean difference in cardiac output is 0 (no difference on average) versus the alternative that there is a difference. The hypotheses to be tested are:H₀:_d= 0versus H_a:_d 0, using a 10% significance level.

Question 9 Subquestions9.a 2 point(s)

The sample meandifferencein cardiac output (Tech AlessTech B) was 2.39standard errors below 0. Provide a complete sketch of thep-value that the supervisor can include in her report. You can use the pval() function in R which will give the exactp-value (and allow you to add your name to the graph when you type 'y' to save the graph to your desktop),or make acompleteby hand sketch and provide the bounds for thep-value. Make sure to include a title for and include your name with your graph.

Student answer No answer entered. 9.b 0 point(s)

You remembersome condition about a normal model required for the t test to be valid and want tocheck this condition. You recall that a QQ plot helps to assess if a population of responses can be considered normally distributed. How many QQ plots do you need to make in this case?

• One QQ Plot of the sample of differences in measurements
• One QQ Plot of the population of differences in measurements
• Two QQ Plots, one for the sample of measurements by Tech A and one for the sample of measurements by Tech B
• Two QQ Plots, one for the population of measurements by Tech A and one for the population of measurements by Tech B

Question 10 Background :

Independent Samples or Paired?

Independent or Paired?For each scenario below determine if it is a paired data scenario or based on two independent samples.

Question 10 Subquestions10.a 2 point(s)

A study was conducted to compare the grade point averages of sophomores who live in campus dormitories with the grade point averages of sophomores who live off campus. Twenty sophomores were randomly selected from campus dormitories at a college, and 20 other sophomores were randomly selected from students who live off campus.

• Paired Data
• Two Independent Samples

10.b 0 point(s)

An experiment was performed to compare the reaction time to two types of traffic signs. One sign type is Prohibitive (e.g., No Left Turn) and the other sign type is Permissive (e.g., Left Turn Only). Ten drivers were used in the study. Each driver was presented with 40 traffic signs, 20 of each type, in a random order. For all 40 signs, reaction time was recorded and the mean of each sign-type calculated.

• Paired Data
• Two Independent Samples

10.c 0.5 point(s)

A study was conducted to evaluate the average gain in strength due to a weight-training program. Thirteen individuals each took a strength test both before and again after they participated in a six-week weight-training program.

• Paired Data
• Two Independent Samples

Question 11 Background :

Which t-test?

Which t test?For each scenario below determine which type of hypothesis test (one-samplettest for a population mean, paired-samplesttest for the population mean difference, or independent-samplesttest for the difference in two population means) should be used to assess each of the following alternative hypotheses.

Question 11 Subquestions11.a 2 point(s)

On average, wives have more years of education than their corresponding husbands.

• one-sample t test for a population mean
• paired-samples t test for the population mean difference
• independent-samples t test for the difference in two population means

11.b 0 point(s)

The average number of years of education for wives is 13.4 years.

• one-sample t test for a population mean
• paired-samples t test for the population mean difference
• independent-samples t test for the difference in two population means

11.c 0.5 point(s)

Theaverage age of persons marrying for the first timein the 1970s was lower than theaverage age of persons marrying for the first timein the 2000s.

• one-sample t test for a population mean
• paired-samples t test for the population mean difference
• independent-samples t test for the difference in two population means