Question

1. For each scenario write the letter for what kind of hypothesis test or confidence interval is described.

A. One sample z for one mean B. One sample t for one mean C. Two-sample t for dependent means D. Two sample t for independent means E. One sample z for one proportion F. Two sample z for two proportions G. None of the above

i. _______ 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.

ii. _______ 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.

iii. _______ 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.

iv. _______ 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.

v. _______ 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.

vi. _______ 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 90% significance.

vii. _______ 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.

viii. _______ 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 ?=0.01.

ix. _______ 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 $62/year with a standard deviation of $12/year. The 50 finance people average $59/year with a standard deviation of $4/year. The standard deviation of the differences is $3.2/year. His confidence interval will be used to accuse the CFO of favoritism.

x. _______ 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.

xi. _______ 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.

xii. _______ 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.

xiii. _______ 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.

xiv. _______ 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.

Answer 1

i. _______ 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.

Answer: A. One sample z for one mean, because the population standard deviation is known

ii. _______ 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.

Answer: F. Two sample z for two proportions

iii. _______ 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.

Answer: D. Two sample t for independent means because the lifestyle of siblings are independent of each other

iv. _______ 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.

Answer: B. One sample t for one mean because population standard deviation is unknown.