Test 2
March 9, 2001 / Name______
Questions 1 - 4 are multiple choice. Circle the letter of the best response. [4 pts each]
1) Suppose you are conducting a test of significance for the weight of Snickers bars. Your null hypothesis is H0: m = 2.5 oz. and your alternative hypothesis is Ha: m < 2.5 oz. You conclude that the mean weight of Snickers bars is less than 2.5 oz. with a P-value of 0.02. Which of the following statements best describes what that P-value means?
a) If the population mean weight of Snickers bars is 2.5 oz. the probability that a sample mean would have a mean as low as the one we found is 0.02.
b) If the population mean weight of Snickers bars is less than 2.5 oz. the probability that a sample mean would have a mean as low as the one we found is 0.02.
c) The proportion of Snickers bars that have weights less than 2.5 oz is 0.02.
d) The probability that the mean weight of Snickers bars is less than 2.5 oz. is 0.02.
2) A confidence interval will increase in width if:
a) Either the sample size increases or the confidence level increases.
b) Either the sample size increases or the confidence level decreases.
c) Either the sample size decreases or the confidence level increases.
d) Either the sample size decreases or the confidence level decreases.
3) Suppose that 50% of all Americans eat three meals a day. You sample 100 Americans and ask each of them, "Do you eat three meals a day?" You then count the number of people that respond yes. This situation is the same thing as drawing from a binomial distribution with what mean and what standard deviation?
a) m = 50, s = 25
b) m = 50, s = 5
c) m = 0.5, s = 0.0025
d) m = 40, s = 0.05
4) You have taken a random sample of 30 grade point averages from Hope College students. You determine that a 95% confidence interval for the mean grade point average is 2.9 to 3.3. Which of the following statements gives a valid interpretation of this interval?
a) 95% of the 30 grade point averages in the sample are between 2.9 and 3.3.
b) 95% of all Hope College students have grade point averages that are between 2.9 and 3.3.
c) If the procedure were repeated many times, 95% of the sample means would be between 2.9 and 3.3.
d) If the procedure were repeated many times, 95% of the time the resulting interval would contain the mean grade point average of all Hope College students.
5) The following two-way table categorizes enrollment at Hope College for last semester.
Let F = a student chosen is a freshman and let W = the student chosen is a woman. Find the following probabilities. (Leave answers in fraction form.) [12 pts.]
CLASS / MEN / WOMEN / TotalFreshman / 297 / 481 / 778
Sophomore / 315 / 429 / 744
Junior / 244 / 408 / 652
Senior / 290 / 429 / 719
Special / 63 / 59 / 122
Total / 1209 / 1806 / 3015
a) P( F and W)
b) P(F | W)
c) P(W | F)
d) P(F or W)
6) A fair eight-sided die has each of the numbers 1, 2, 3, 4, 5, 6, 7, and 8 on its faces. It is rolled 3 times. [10 pts.]
a) What is the probability that exactly one 8 shows?
b) What is the probability that at least one 8 shows?
7) Suppose there are two events A and B. Suppose P(A) = 0.3 and P(B) = 0.2. Find P(A and B) for the following two situations. [8 pts]
a) Events A and B are independent.
b) Events A and B are disjoint.
8) According to Mars Incorporated, the maker of m&m's, 30% of the regular m&m's are brown. (The remaining 70% are green, red, yellow, blue or orange.) Suppose that 3 m&m's were chosen at random. Complete the following probability distribution where X is the number of brown m&m's and P(X) is the probability of obtaining exactly X brown m&m's in your sample. [8 pts.]
X / 0 / 1 / 2 / 3P(X)
9) According to the Public Health Service 35% of American adults do not drink alcohol.
a) If a random sample of 10 Americans is taken, what is the probability that exactly 3 do not drink alcohol? [6 pts.]
b) If a random sample of 10 Americans is taken, what is the probability that at least one of them does not drink alcohol? [6 pts.]
10) The weights of newborn children in the United States vary according to the normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds.
a) What is the probability that a baby chosen at random weighs more than 7 pounds? [6 pts.]
b) You choose 10 babies at random. What is the probability that their average birth weight is more than 7 pounds? [6 pts.]
11) A friend who hears that you are taking a statistics course asks for help with a chemistry lab report. She has made six independent measurements of the specific gravity of a compound and found the sample mean to be 3.70. The lab manual says that repeated measurements will vary according to a normal distribution with standard deviation s = 0.12. [12 pts.]
a) Find a 95% confidence interval for the mean specific gravity, m, of the compound.
b) What size sample would be needed in order to estimate m within ±0.05 with 95% confidence?
12) Suppose sonnets by Shakespeare are known to contain an average of m = 6.5 new words (words not previously used in his sonnets). The standard deviation of the new words is s = 2.7. A new manuscript with 5 new sonnets is found and scholars are debating whether or not they belong to Shakespeare. The new sonnets contain an average of new words not used previously by Shakespeare. Does this sample mean differ enough from the population mean to give evidence that Shakespeare was not the author of these new sonnets? (Use a = 0.05.) Make sure you include the hypotheses, test statistic, P-value, and conclusion. [10 pts]
Questions from chapters 7 and 8
1) A large elementary school has 15 classrooms, with 24 children in each classroom. A sample of 30 children is chosen by the following procedure. Each of the 15 teachers selects 2 children from his or her classroom to be in the sample by numbering the children from 1 to 24, then using a random digit table to select two different random numbers between 01 and 24. The 2 children with those numbers are in the sample. Did this procedure give a simple random sample of 30 children from the elementary school?
a) No, because the teachers were not selected randomly.
b) No, because not all possible groups of 30 children had the same chance of being chosen.
c) No, because not all children had the same chance of being chosen.
d) Yes, because each child had the same chance of being chosen.
e) Yes, because the numbers were assigned randomly to the children.
2) A study is conducted to determine if one can predict the number of traffic accidents based on the amount of snowfall. The response variable in this study is
a) the amount of snowfall.
b) the number of traffic accidents.
c) the experimenter.
d) the age of the driver or any other variable that may explain the an accident.
e) none of the above.