Section I - Multiple Choice
1. (4 points) A frequency distribution is a tabular summary of data showing the
a. fraction of items in several classes
b. percentage of items in several classes
c. relative percentage of items in several classes
d. number of items in several classes
2. (4 points) Which of the following arguments is true about the level of significance ofO for hypotheses test?
g. The probability of rejecting fin (null hypotheses) when H (alternative hypotheses) is true is ‹I .
b. The probability of rejecting Pte (null hypotheses) when loo is true is H .
c. The probability of failing to reject do when Ho is true is O .
d. The probability of failing to reject to when th is true is If .
3.(4 points) Variance is
a measure of the average, or central value of a random variable
b.a measure of the dispersion of a random variable
c.the square root of the standard deviation
d.the sum of the squared deviation of data elements from the mean
4. (4 points) For a continuous random vañable x, the height of the function at x is a the probability at a given value of x
b. 0.50, since it is the middle value
c. a value less than zero
d. named the probability density function f(x)
5. (4 points) From a population that is normally distributed, a sample of 30 elements is selected. The sample meanF is 20 and the sample standard deviation s is also 20. For the interval estimation off , the proper distribution to use is
m normal distribution
b. t distribution with 29 degrees of freedom
c. t distribution with 19 degrees of freedom
d. none of the above
6. (4 points) It is reported that 10% of all merchandise sold in the United States gets returned. A Houston department store sampled 100 items sold in January and found that 15 of the items were returned. The interest is to determine whether the return percentage of Houston store is different from the returns for the nation as a whole. For this problem the parameter of interest is
a.
b. p
d. fit
7. (4 points) For the hypothesis test to : N @ ; ffa : > Jp ,’ the test statistic based on the Z-test is determined to be z — 1.06. The sample size has been 24. The p-value for tiiis test is
a 0.15
b. 0.85
c. 0.8554
d. 0.1446
8. (4 points) For confidence interval, as the sample size increases, the length of confidence interval
m increases
b. decreases
c. stays the same
d. increases or decreases depending on the size of the mean
9. (4 points) It is known that the population variance is 144. At 95% confidence, what size sample should be taken so that the margin of error is docs not exceed 5 or less?
m 22
b. 23
d. 25
10. (4 points) Since the population size is always larger thun the sample size, then the sample statistic
a. can never be larger than the population parameter
b. can never be equal to the population parameter
c. can be smaller, larger, or equal to the population parameter
d. none of the above
Sectton II - Short Amer
11. The probability distribution for the number of goals the Lions soccer team makes per game is given below
Number of goals Probability
0 0.05
1 0.15
2 0.35
3 0.30
4 0.15
a. (5 points) What is the probability that in a given game the lions will score at least 1 goal?
b. (5 points) What is the expected number of goals per game?
c. (5 points) Compute the variance and standard deviation for the number of goals the Lions soccer team makes per game.
12,
A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 10.
a. (6 points) Thc professor hes informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?
b. (6 points) If 12.1 percent of her students failed the course and received F’s, what was the maximum score among those who received an F7
c. (6 points) lf 33 percent of the students received grades of B or better (i.e., A's and B's), what is the
minimum score of those who received a B7
13 In order to detcmiine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. It was determined that the students in the sample spent an average of 14 hours with a standard deviation of 3.2 hours watching TV per week.
a (6 points) Provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week.
b. (6 points) Assume that a sample of 62 students was selected (with the same mean and the standard
deviation). Provid* a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching TV per week.
14 A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. A random sample of 49 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.88 ounces with a standard deviation of 0.35 ounces.
a. (5 points) Formulate the hypotheses to test to determine if the machine is in perfect adjustment.
b. (5 points) Compute the value of the test statistic.
c. (5 points) Compute the p-value •nd give your conclusion regard ng the adjus °ent °* >• machine. Let
= .03.
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