PRACTICE TEST #2
32. Is there good evidence at the 5% level of significance that the mean decibel level in corridors of hospitals is not 55 decibels? Assume the population standard deviation and data given in #30.Make sure to give the table number and the data number and the yes/no answer.
33. Give the p-value for #32 and say what it means in everyday terms.
34. Suppose the question in #32 is done again with another set of data, what is the chance that it will be concluded that the mean not 55 when it actually is?
35. Suppose the question in #32 is done again with another set of data, what is the chance that it will not be concluded the mean differs from 55 when it actually does?
36. Is there good evidence at the 5% level of significance that the mean decibel level in corridors of hospitals is over 55 decibels? Assume the population standard deviation and data given in #30.Make sure to give the table number and the data number and the yes/no answer.
37. Give the p-value for #36 and say what it means in everyday terms.
40. Suppose a different set of data was used to answer #32 and the p-value was .163.
A) Would the answer to #32 be yes or no?
B) What if the significance level was 1% instead, would the answer be yes or no?
C) What if the significance level was 20% instead, would the answer be yes or no?
D) What if the significance level was 10% instead, would the answer be yes or no?
42. 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 mean date for all possible years (see #29 on practice tests).
43. Is there good evidence at the 1% significance level that the mean ice break day for all possible years is not May 3 (corresponds to 33)? Use the data in #42. Make sure to give the table number and the data number and the yes/no answer.
44. Give the p-value for #42 and say what it means in everyday terms.
45. Can we prove at the 5% significance level that the average age of students at a certain university is less than 24 years? Data: a SRS of 17 students with a sample mean age of 22.8 years and a sample standard deviation of 3.1 years. Make sure to give the table number and the data number and the yes/no answer.
46. Give the p-value for #45 and say what it means in everyday terms.
48. Can we prove at the 10% significance level that secretaries will type faster using a new computer keyboard? Assume normal populations and use the data given here:
SRS of 10 secretaries, half tried the new keyboard first, the other half tried the standard keyboard first. Words per minute are given.
Secretary / A / B / C / D / E / F / G / H / I / JOld Keyboard / 73 / 82 / 95 / 107 / 92 / 111 / 83 / 72 / 68 / 85
New Keyboard / 78 / 90 / 105 / 103 / 90 / 116 / 92 / 88 / 75 / 93
Make sure to give the table number and the data number and the yes/no answer.
49. Give the p-value for #48 and say what it means in everyday terms.
50. Suppose data from 10 different secretaries are used to answer #48 (instead of the data given), what is the chance we won’t conclude the new keyboard is better when it actually is?
51. Suppose data from 10 different secretaries are used to answer #48 (instead of the data given), what is the chance will conclude the new keyboard is better when it actually is not?
52. Using the data in #48 give a 99% CI for the mean improvement for all possible secretaries when it comes to using the new keyboard.
53. Can we prove at the 5% significance level that Colorado high school football teams score a different number of points on average in their first game of the year as compared to their last? Assume normal populations and use the data given here: SRS of 6 teams from 2008 season. Make sure to give the table number and the data number and the yes/no answer.
Team / Fruita / CanonCity / Ft Lupton / Liberty / Delta / AspenPoints in first game / 35 / 44 / 6 / 41 / 25 / 65
Point in last game / 7 / 3 / 27 / 51 / 52 / 13
54.Give the p-value for #53 and say what it means in everyday terms.
55. Can we prove at the 5% significance level that gas prices are lower this month than last month? Use the data given here. Assume normal populations and SRSs. Make sure to give the table number and the data number and the yes/no answer.
This month / Last month2.09, 2.19, 2.19, 2.14, 2.22 / 2.55, 2.49, 2.59, 2.59, 2.29, 2.39
56.Give the p-value for #55 and say what it means in everyday terms.
57. Give a 95% CI for the mean decrease is gas prices for all gas stations from last month using the data in #55.
58. Can we prove at the 1% significance level that the mean number 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 agoSRS of 51 games / SRS of 56 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
59.Give the p-value for #58 and say what it means in everyday terms.
60. We wish to estimate with a 90% CI the percentage of all field mice that carry a certain disease to within 5%. How large a sample should we get if we have no idea what the percentage might be?
61. We wish to estimate with a 90% CI the percentage of all field mice that carry a certain disease to within 5%. How large a sample should we get if we have good reason to believe the percentage is around 20%?
62. Photos are taken of drivers on a certain road to determine if they are wearing their seatbelts. Give a 99% CI for the percentage of all drivers that would drive on this road that will have their seatbelts on. A sample of 630 photos showed 440 with seatbelts on.
63. See #62, can we show at the 5% significance level that the percentage of all drivers that would drive on this road that would have their seatbelts on is over 60%? Make sure to give the table number(s), data number, yes/no answer.
64. See #62, can we show at the 5% significance level that the percentage of all drivers that would drive on this road that would have their seatbelts on is not 60%? Make sure to give the table number(s), data number, yes/no answer.
65. Give the p-value and explain its meaning in everyday terms for #64.
66. Photos are also taken on another road in another state (see #62) and a sample of 500 photos showed 324 with their seatbelts on. Give a 95% CI for how much higher the percent wearing seatbelts is on the first road.
67. See #62 & #66, can we prove at the 1% significance level there is any difference in the percentage wearing seatbelts between the two roads? Make sure to give the table number(s), data number, yes/no answer.
68. See #62 & #66, can we prove at the 1% significance level the percentage wearing seatbelts is higher on the first road? Make sure to give the table number(s), data number, yes/no answer.
69. Give the p-value and explain its meaning in everyday terms for #68.