Stat 4220 Homework due April 10

1.  For each scenario write the letter for what kind of hypothesis test or confidence interval is described
Hint: You will use each letter either twice or never.

  1. One sample z-score for a mean
  2. One sample t-score for a mean
  3. Matched pairs difference in means
  4. Two sample z-score means independent
  5. Two sample t-score means independent
  6. One sample z-score for a proportion
  7. One sample t-score for a proportion
  8. Two sample z-score for p1-p2
  9. None of the above

  1. ______An anthropology major believes the distribution of homes per city from the Anasazi Indians is normally distributed with a standard deviation of 12 homes. A random sample of 10 Anasazi cities shows an average of 46 homes. He wants an 85% confidence interval for the true overall average.
  1. ______A History major suspects that Paris has more criminals today than it did in 1500. She learns that in 1500 there were 200 thousand people, and 2 thousand criminals. Today there are 2,211 thousand people, and 30 thousand criminals. She wonders if the difference is significant.
  1. ______An international studies student has found 90 families where one sibling is living in the US and the other sibling is living in China. The average for the US siblings is 195 pounds with a standard deviation of 20 pounds. The average for the Chinese sibling is 180 pounds with a standard deviation of 15 pounds. The standard deviation of the difference across siblings was 8 pounds. She plans on writing a book discussing whether this is evidence that the American lifestyle is more fat than the Chinese lifestyle.
  1. ______A psychology major wants to know how much money it would take before a person would do the Macarena in Prexy’s Pasture. He randomly samples 20 people and gets an average of $30 with a standard deviation of $90. He wants to use 93% confidence.
  1. ______A criminal justice major wants to know the average time a drug dealer spends in jail in Colorado. The mayor says it should be longer than 15 years. Assume the distribution is normal. A random sample of 10 convicted drug dealers has an average of 20 years with a standard deviation of 5 years. The goal is to test the mayor’s claim.
  1. ______A theater and dance major wants to know if more women or men have seen a ballet. He randomly samples 200 women and finds 11% have seen a ballet. He samples 200 men and finds 7% have seen a ballet. He wants to use a 10% significance test.
  1. ______A communication major wants to know the average blood pressure for someone who is about to give a speech. He randomly samples 40 people before they give a speech and gets an average systolic blood pressure of 190 with a standard deviation of 30 mmHg. He wants a 98% confidence interval for the true average systolic blood pressure of someone who is about to give a talk.
  1. ______An art major is testing whether a new painting was made by Michelangelo. It is known that the amount of lead in a square inch of any of Michelangelo’s paintings has a mean of 82 ppm and a standard deviation of 13 ppm. On the new painting 60 random square inches are selected, and there is an average of 70 ppm of lead per square. She wants to test if this painting has significantly different lead levels on average using α=0.01.
  1. ______An accounting major knows the marketing people are getting paid more than the finance people. He wants a 96% confidence interval for the difference in salaries between the two majors. The 80 marketing people average $62K/year with a standard deviation of $12K/year. The 50 finance people average $59K/year with a standard deviation of $4K/year. The standard deviation of the differences is $3.2K/year. His confidence interval will be used to accuse the CFO of favoritism.
  1. ______A philosophy major wants to estimate the proportion of people who know what a philosophy major does with 95% confidence. He randomly samples 100 people and exactly half know what he does.
  1. ______A political science major wants to know whether more than half the people in Laramie vote on election day. A random sample of 350 people showed 185 of them voted.
  1. ______A journalism major is tracking the number of protests between San Francisco and New York. He randomly selects 100 days and find the number of protests in each city on each of those days. The average in New York was 2.4 protests, the average in San Francisco was 0.7 protests. The standard deviation in New York was 2.3 while in San Francisco it was 5.7 and the standard deviation of the differences was 1.2 protests. His goal is to find with 80% confidence what the average difference is in the number of riots between the two cities.
  1. ______A biology major wants to know the difference between spraying your counter with Lysol and spraying it with alcohol. A petri dish with a million bacteria on it had 99% of the germs die with Lysol. A different dish with a million bacteria on it had 80% die with alcohol. He wants a 95% confidence interval for the true population difference.
  1. ______An English major thinks contemporary books have more words than they did 50 years ago. She randomly selects 40 books that were written this year, and randomly selects 40 books written 50 years ago. Her data shows that modern books have an average of 140 thousand words with a standard deviation of 70 thousand words. Fifty years ago it was an average of 90 thousand words with a standard deviation of 10 thousand words. She wants a test with 10% significance.

2.  80 random men and 70 random women were sent to visit the orthodontist for the first time. 61 of the men and 54 of the women came back with braces. Write the equation for the 96% confidence interval of difference in the proportions of men and women who will get braces at the orthodontist. Use the numbers given in the problem without simplifying (except for the z or t score). You do not need to solve it out.

3.  The Branding Iron says the average salary for a UW graduate is higher than the salary of a CSU graduate. Test at the 10% significance level if this is true given the data below.

Survey of UW graduates:

Participants: 32 Cowboys

Average Salary: $66,500

Standard Deviation for each Cowboy: $10,000

Survey of CSU graduates:

Participants: 32 Rams

Average Salary: $59,500

Standard Deviation for each Ram: $8,000

Pooled standard deviation for each graduate: $9,000

Matched Pairs standard deviation for each graduate: $8,522

Average standard deviation for both graduates: $9,000

4.  Harry Potter believes that he can tell if a person is a bad guy by listening to the background music when they come near. To find out if this is the case, Harry records what type of music he hears around 124 random people. Then Harry performs the Crucius curse to determine if the person is a good guy or bad guy. Based on the following data, determine if the proportion of good guys with ominous music differs from the proportion of bad guys with ominous music.

Allegiance
Good Guys / Bad Guys
Background
Music / Ominous Music / 45 / 16
Happy Music / 38 / 25

5.  The Statistics Department really wants to make sure the students fill out the on-line evaluations. They realize students are often frustrated with tricky questions that cannot be done, but the evaluations are so important they survey 28 students in Dr. Crawford’s class, and 19 students in Michele’s class. The department wants to know if certain teachers are more effective at getting their students to complete the evaluations. The results are shown below:

Class
Crawford / Michele
Did you fill out the online evaluation? / Yes / 16 / 8
No / 12 / 11

Find a 95% confidence interval for the difference in proportions of students in each class who filled out the on-line class evaluation.

6.  Santa Claus suspects that calculators are the perfect Christmas gift. To test this he gives a calculator to 16 college students, but gives an X-box to 16 other students. Then Santa watched their average GPR for the year. Use α=0.25. Assume grades are normally distributed with equal variance for both groups. Do a hypothesis test (all the steps) on whether a calculator increases GPR more than an X-box does.

Students which got a calculator

Number: 16

Mean GPR for the year: 3.2175

Standard deviation (per GPR): 0.8

Students which got an X-box

Number: 16

Mean GPR for the year: 2.92

Standard deviation (per GPR): 1.5

The pooled standard deviation is 1.15

The matched pairs standard deviation is 1.07

7.  Brent wonders why his Pop-Tarts are always burnt, when Mason’s seem to be just right. He thinks it might be because his outlets are getting more voltage than Mason’s outlets. To test this, he gets all the multimeters he can find. Then Brent takes the multimeters to each house and randomly selects and electric outlet. The voltage levels are shown below. Assume it is normally distributed.

Burn level / Brent / Mason
Multimeter 1 / 12 / 15
Multimeter 2 / 15 / 15
Multimeter 3 / 17 / 18
Multimeter 4 / 13 / 11
Multimeter 5 / 11 / 16
Multimeter 6 / 18 / 22
Multimeter 7 / 15 / 14

With α=.10 test whether the voltage is more at Brent’s house then at Mason’s house.

8.  A study asked 800 married men if they would be willing to carry their wife’s purse through the store. 720 of them said they were willing. Find a 90% confidence interval for the proportion of men who said they would carry the purse.

9.  The average interest rate for 10 year CD is an interesting measure for how the economy is doing. A study group examined 42 banks and found an average 10 year CD rate of 0.03 with a standard deviation of 0.001. Calculate the 99% confidence interval for the true average 10 year CD rate across the nation.

10.  Wheel thickness on a train is random because wear and tear causes the wheel to wear down. The distribution of wheel thickness is known to have a standard deviation of 0.14 inches. The average wheel thickness tells you how old the train is. A random sample of 6 wheels on the Laramie Express Train found an average wheel thickness of 3.22 inches. Find a 99.9% confidence interval for the true average wheel thickness on the Laramie Express.

11.  A study on children diagnosed with Deliops disease examined whether taking garlic pills would prolong the life of the children. The children who did not take garlic lived an average of 4 years. Children who took the garlic pills lived an average of 21 years. The confidence interval for the difference in average for the non-garlic pills verses garlic pills was (-9, 43) years.

What would you conclude about the effectiveness of garlic pills?

12.  We would like to compare married and unmarried people with regard to their answer to the question “Do you think that marriage as an institution is becoming obsolete?” We sampled 150 married adults, and 175 unmarried adults. Of the married adults, 31% answered ‘yes’ to this question, and of the unmarried adults, 46% answered ‘yes’. Provide a 99% confidence interval to estimate the true difference in the married and unmarried proportions who would answer ‘yes’ to this question.

13.  We also polled single parents who had never been married and cohabiting parents. Out of the 90 parents who had never been married, 52 answered ‘yes’, and out of the 120 cohabiting parents, 74 answered ‘yes.’ Test the claim that the proportion of single (never married) parents is different from the proportion of cohabiting parents.

14.  In 2011 a sample of 345 parents had 162 which said children should be financially independent from their parents by the age of 22.

  1. Provide a 90% confidence interval for the true proportion of all parents in 2011 who believe children should be financially independent by age 22.
  1. In 1993 the proportion was 80%. Does your confidence interval indicate that the proportion who would say this in 2011 is different from who said this in 1993?

15.  A sample of 808 young adults found that 22% say they will wait to have a baby because of the economy. A sample of 100 elderly people found that 86% suggested young people should wait to have a baby because of the economy. Test the claim that the proportion of young adults is different from the proportion of elderly people who think waiting to have a baby is a good idea.

16.  A study investigated the link between speed of an automobile at the time of a crash, and the cost of the insurance claim. Below is the residual plot and the output from Excel.

a)  Are there any assumptions for regression that you feel ought to be examined?

b)  Test at the 5% significance level whether increased speed relates to higher claim cost.