Stats exam 3 quiz questions
In 2012, the General Social Survey included a question that asked respondents if they had "often/sometimes" been the subject of gossip at work. Out of 606 men, 75 said yes they had "often/sometimes" been the subject of gossip at work. Out of 580 women, 67 said yes they had "often/sometimes" been the subject of gossip at work. What is the pooled proportion for the null hypothesis Ho:p1-p2=0 vs. alternative hypothesis Ha: p1-p2 does not equal 0?
0.120
In Spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how many hours they had exercised in the past 24 hours. For the 39 randomly selected upperclassmen, the sample mean was 0.76 and sample standard deviation was 0.75. For the 35 randomly selected underclassmen, the sample mean was 0.60 and the sample standard deviation was 0.73. What is the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen?
0.16
A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Has there been improvement? (pre-post) What value of t would you use for the 95% confidence interval?
2.776
Which of the following are assumptions for the confidence interval for the different between two population means?
Both sample sizes are greater than 30 or the data from a Normal Distribution Data is Quantitative. Random Sample
When we make inferences about the difference of two independent population proportions, what assumptions do we need to make?
Counts of successes and failures at least 15 each for each group. Random samples.
In 2010 and 2012, Gallup asked the same 50 people how many hours had they worked at a job in the past 7 days. Is there a difference in the population mean amount of hours worked at a job between 2010 and 2012? Would this be an example of independent or dependent samples?
Dependent Samples
A significance test is conducted to determine if the majority of students at UF have a paying job at some time during the year. Ho: p=0.5 vs Ha: p>0.5 What would a Type I Error mean in this setting?
Determining that it is more than half of students in the population who have a job when in fact, it is really not.
A teacher wants to see if a new unit on fractions is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Suppose that you are about to compute a confidence interval for μ d, how do you check for normality?
Find the difference between the two scores for each subject. Make a plot of the differences and check for outliers.
A staff member at UF's Wellness Center is interested in seeing if a new stress reduction program will lower employees high systolic blood pressure levels. Twenty people are selected and have their blood pressure measured. Each person then participates in the stress reduction program. One month after the stress reduction program, the systolic blood pressure levels of the employees were measured again. Did the program reduce the average systolic blood pressure level? (mud = population mean difference = before - after)
Ha: mud > 0 We are interested in seeing if the after value is lower than the before value. So, when we take before - after we get a positive value. So, this should be mud 0.
A small county has two property appraisers, Tim and Julie. Does Tim appraise property differently on average than the Julie? Each appraiser looks at 20 properties and each independently determines the value of the property. (Tim - Julie) How should we write the alternative hypothesis?(mud is the population mean difference)
Ha: mud does not equal zero
Do men and women save different amounts of money? A study asks 100 randomly selected men and women between the ages of 25 and 60, "How much they saved in a savings account or similar type account in the past six months?" How should we write the alternative hypothesis? Let mum = population mean amount saved for men and muw = population mean amount saved for women.
Ha: mum - muw does not equal 0
Do less Republicans (group A) than Democrats (group B) favor the government investing billions of dollars to improve the country's train system? One thousand Republicans and one thousand Democrats were asked if they favored spending billions to improve the country's train system. How would we write the alternative hypothesis?
Ha: pA - pB < 0
Do less Republicans (group A) then Democrats (group B) favor the government investing billions of dollars to improve the country's train system? One thousand Republicans and one thousand Democrats were asked if they favored spending billions to improve the country's train system. How would we write the alternative hypothesis?
Ha: pA - pB < 0
Now change the value of n and notice what happens to the Type I and II Errors. Which of the following is the best description of the effect of increasing n?
Probability of Type I Error does not change - that is given by alpha. But as the sample size n increases, the Probability of a Type II Error decreases, making it easier to make a correct decision to Reject Ho.
What is the definition of Type I error?
Rejecting the null hypothesis when the null hypothesis is really true.
A social scientist is interested in determining if there is a significant difference in the proportion of Republicans between two areas of town. He takes independent random samples of 200 families in each area of town and a significance test was conducted. The p-value was 0.016. What should be our conclusions?
The evidence is pretty strong - there is a difference in the proportion of Republicans between the two areas of town.
A staff member at UF's Wellness Center is interested in seeing if a new stress reduction program will lower employees high blood pressure levels. Twenty people are selected and have their blood pressure measured. Each person then participates in the stress reduction program. One month after the stress reduction program, the blood pressure levels of the employees were measured again. Did the program reduce the average blood pressure level? The 95% confidence interval was (5.6, 10.2). What can we expect will be the p-value for a two sided test using this data?
The p-value should be smaller than 0.05.
An education specialist was studying SAT math scores at a local university. She found the following 95% confidence interval for the population mean score for SAT math: (450, 550). Suppose that a significance test at Ho:population mean = 475 versus Ha: population mean does not equal 475. The p-value for this test was 0.14. Which of the following statements accurately describes this situation?
The population mean score for SAT Math is NOT statistically or practically different from 475.
Is the right arm or left arm stronger? Twenty five right handed people were studied. They were asked to do as many bicep curls as possible, first with their right arm and then with their left arm. Note:The differences were calculated as right-left. The 95% confidence interval for the true mean difference is (-9.242, 0.2472). Which of the following statements is the correct interpretation?
There is not convincing evidence that the population mean number of bicep curls for the right arm is different from the population mean number of curls than the left arm, at 95% confidence.
An agricultural field test compares two varieties of corn, silver queen and country gentlemen. The researchers take 10 plots and divide each of these plots in half. Each plot has a similar amount of sun light, shade, quality of soil and irrigation. The variety of corn is randomly chosen for each half of a plot. After the harvest, the yield of corn is measured for each half plot at each location. The yield from silver queen was compared to the yield of country gentlemen. Note: Differences were taken by taking Variety A - Variety B.The 95% confidence interval for the mean is (-0.223, 0.988).What is the correct interpretation of this interval?
There is not enough evidence to say that variety A has a different mean yield than variety B, at 95% confidence.
In 2012, Gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that random samples of 100 respondents were selected from both Vermont and Hawaii. From the survey, Vermont had 65.3% who said yes and Hawaii had 62.2% who said yes. What is the value of the population proportion of people from Hawaii who exercised for at least 30 minutes a day 3 days a week?
Unknown
A major grocery store chain is trying to cut down on waste. Currently, they get peaches from two different distributors, Whole Fruits and Green Grocer. Out of a two large shipments, the manager randomly selects items from both suppliers and counts the number of items that are not sell-able due to bruising, disease or other problems. She then makes a confidence interval. Is there a significant difference in the quality of the peaches between the two distributors?95% CI for pW-pG:(0.064, 0.156)
We are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 and 0.156 HIGHER than the proportion of non sell-able items for Green Grocer.
A university administrator was interested in determining if there was a difference in the distance students travel to get from class from their current residence(in miles). Men and women at UF were randomly selected. The Minitab output is below. What is the best interpretation for the output?Difference = mu (F) - mu (M)T-Test of difference = 0 (vs not =): T-Value = -1.05 P-Value = 0.305 DF = 21
With a p-value of 0.305, we do not have statistically significant evidence that the population mean distance traveled to class is different for men and women at UF.
Should we focus on the p-value instead of the alpha level?
Yes - alpha is arbitrary, while the p-value gives a better representation of the amount of evidence we have to reject the null.
Doctors are interested in seeing if lifting weights to alleviate back pain is effective. Twenty five volunteers are asked to rank their level of pain on a scale from one to ten. For the next two months, they then exercise for 2 months with a physical therapist. The volunteers focus on different weight lifting exercises that strengthen the back. Twenty five volunteers are again asked to rank their level of pain on a scale from one to ten. Was the amount of pain less after completing the exercises? What type of test would they conduct to test this claim?
comparing means from dependent samples
The issue of capital punishment is a hotly debated topic. Do more Republicans than Democrats support capital punishment? A researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. In this problem, we want to make inferences about:
comparing proportions from two independent samples
When conducting a significance test to determine if there is a difference between two treatments, with a quantitative response variable, treatments are given to different experimental units, we summarize the data by:
computing the mean and standard deviation of each treatment group separately.
Do college students hourly wages tend to go up during their college years? One hundred people were asked for their hourly wage during their freshman year of college and then their senior year of college.
means from dependent samples
Do people improve their timing on an online crossword puzzle with an additional attempt? Twenty people were timed to complete a crossword puzzle online. After a twenty minute break, they were asked to complete the crossword puzzle online again. Was there an improvement in their time? (first - second) The p-value was 0.12. Interpret. With a p-value of 0.12, we have [ Select ]statistically significant evidence that the [ Select ] time to complete the puzzle has improved.
no population mean
What is the typical hourly wage for college students?
one mean
A University of Florida study on drinking habits asks a random sample of students if they drink any alcohol when they party. We want to extend the results to all students at the university. In this problem, we want to make inferences about:
one proportion
What proportion of college students have a full time job?
one proportion
In Spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how many hours they had worked the previous day. The 95% confidence interval comparing underclassmen to upperclassmen was (-0.233, 1.1250) Interpret the interval. "We are 95% confident that the [ Select ] hours of work for underclassmen is between 0.233 [ Select ]to 1.125 [ Select ] that upperclassmen."
population mean less more
Do college students opinions about health insurance change during their college years? One hundred students were asked as freshman and then as seniors if they supported or opposed the Affordable HealtCare Act.
proportions from dependent samples
Is there a difference in the hourly wage of male and female college students?
two independent means
Is there a difference in the number of male and female college students that have a full time job?
two independent proportions
