Practice test #4



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PRACTICE TEST #4
6. Medicine: In order to test a new drug for adverse reactions, the drug was administered to 1200 test subjects with the following results: 70 reported that their only adverse reaction was loss of appetite, 120 reported only loss of sleep, and 800 reported no adverse reactions.

A) If a randomly selected test subject suffered loss of appetite, what is the probability that the subject also suffered loss of sleep?

B) If a randomly selected test subject suffered loss of sleep, what is the probability that the subject also suffered loss of appetite?

C) If a randomly selected test subject did not suffer a loss of appetite, what is the probability that the subject suffered loss of sleep?

D) If a randomly selected test subject did not suffer loss of sleep, what is the probability that the subject suffered a loss of appetite?
7. Politics: In a given county records show that of the registered voters, 45% are Democrats, 35% are Republicans, and 20% are Independents. In an election, 70% of the Democrats, 40% of the Republicans, and 80% of the Independents voted in favor a parks and recreation bond proposal. If a registered voter chosen at random is found to have voted in favor of the bond:

A) What is the probability that the voter is a Republican?

B) What is the probability that the voter is a Democrat?

C) What is the probability that the voter is an Independent?


8. In a survey of subscribers of Fortune Magazine, 72% rented a car for either personal or business reasons in the last 12 months, 54% rented a car for business reasons, 51% for personal reasons.

A) What is the probability a subscriber rented a car for business reasons and personal reasons?

B) What is the probability a subscriber did not rent a car in the last 12 months?

C) What is the probability a subscriber rented a car for business reasons only in the last 12 months?


9. During the winter Moe experiences difficulty in starting his two cars. The probability the first car starts is 0.85 and the probability the second car starts is 0.60. There is a 0.48 probability that both start.

A) What is the probability that at least one car starts?

B) What is the probability that neither starts?

10. A survey of automobile ownership was conducted for 200 families in Denver. The results of the study showing ownership of automobiles of US and foreign manufacturers follows:






Own a US car

Do not own a US car

Totals

Own a foreign car

28

9

37

Do not own a foreign car

155

8

163

Totals

183

17

200

A) What is the probability that a family owns both a US and a foreign car?

B) What is the probability that a family owns a car, US or foreign?

C) If a family owns a US car, what is the probability it also owns a foreign car?

D) If a family owns a foreign car, what is the probability it also owns a US car?

E) Are US and foreign car ownership independent? Explain.


13. Pregnancy Testing: A new pregnancy test was given to 150 pregnant women and 120 women that were not pregnant. The test indicated pregnancy in 93% pregnant women and 9% of the women that were not pregnant. Pick a woman at random from the 270 women that were studied:

A) If the test indicates she is pregnant, what is the probability that she is pregnant?

B) If the test indicates she is not pregnant, what is the probability that she is not pregnant?
14. A certain football team plays 55% of its games at home and 45% away. Given that the team has a home game, there is a 0.80 probability that it will win. Given that it plays away, there is a 0.65 probability that it will win. What percent of the games does the team win?

15. An oil company drills wells in search of oil. The chance that a drilled well will be a producer well is 15%.



  1. If 12 wells are drilled, what is the probability that all 12 will be producer wells?

  2. If 12 wells are drilled, what is the probability that all 12 will be dry?

  3. If 12 wells are drilled, what is the probability that exactly 1 will be a producer well?

  4. If 12 wells are drilled, what is the probability that at least 3 of the wells are producer wells?

  5. Suppose 1000 wells are drilled, what is the probability that at least 155 will be producer wells? First find the mean and standard deviation in the number of producer wells in samples of 1000 wells.

16. Suppose a license plate is 3 letters followed by three numbers.

a) How many license plates are possible if there are not repeated letters or numbers?

b) How many license plates are possible if there are repeats allowed?


17. From a standard 52 card deck, how many 5 card hands will have all hearts?

70. There is a contest in Alaska which people predict the time and date the ice will break up on a certain spot on a certain river. It’s called the Nenana Ice Classic. Here is the data of the ice breaks for past years. First change the data to numbers that represent days after March 31st. So April 1 will be a 1 and April 28 a 28 and May 1 a 31 and May 20 a 50 etc. We are curious about the date of the ice break.

April 20: 1940, 1998 April 23: 1993 April 24: 1990, 2004

April 26: 1926, 1995 April 27: 1988, 2007 April 28: 1943, 1969, 2005

April 29: 1939, 1953, 1958, 1980, 1983, 1994, 1999, 2003

April 30: 1917, 1934, 1936, 1942, 1951, 1978, 1979, 1981, 1997

May 1: 1932, 1956, 1989, 1991, 2000

May 2: 1960, 1976, 2006 May 3: 1919, 1941, 1947 May 4: 1944, 1967, 1970, 1973

May 5: 1929, 1946, 1957, 1961, 1963, 1987, 1996

May 6: 1928, 1938, 1950, 1954, 1974, 1977 May 7: 1925, 1965, 2002

May 8: 1930, 1933, 1959, 1966, 1968, 1971, 1986, 2001

May 9: 1923, 1955, 1984 May 10: 1931, 1972, 1975, 1982

May 11: 1918, 1920, 1921, 1924, 1985 May 12: 1922, 1937, 1952, 1962

May 13: 1927, 1948 May 14: 1949, 1992

May 15: 1935 May 16: 1945 May 20: 1964
Give a 90% CI for the standard deviation for all possible years (see #22 on practice tests).
71. See #70, can we prove at the 5% significance level that standard deviation for all possible years is over 5 days? Make sure to give the table number(s), data number, yes/no answer.

72. See #70, can we prove at the 5% significance level that standard deviation for all possible years is not 5 days? Make sure to give the table number(s), data number, yes/no answer.


73. Give the p-value and explain its meaning in everyday terms for #72.
74. Can we prove at the 10% significance level that the standard deviation of points scored in a game in a basketball league differs from 10 years ago? Use the data given here. Make sure to give the table number and the data number and the yes/no answer.

This year

10 Years ago

SRS of 61 games

SRS of 26 games

Sample mean of 202 points per game

Sample mean of 199 points per game

Sample standard deviation of 19 points per game

Sample standard deviation of 17 points per game


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