Assignment:
Exhibit 1-1
A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below:
Number of
Breakdowns Probability
0 0.12
1 0.38
2 0.25
3 0.18
4 0.07
1. Refer to Exhibit 1-1. The expected number of machine breakdowns per month is
a. 2
b. 1.70
c. one, since it has the highest probability
d. at least 4
2. During the last 10 years marketing executives believed that the same proportion of adult men and adult women watched TV news programs. Current information indicates there has been an increase in the percentage of women watching TV news programs. The marketing executives would like to perform astatistical test to assure themselves that a greater proportion of women now watch TV news programs than men. What should be used for the Null and Alternative hypotheses to perform this test?
Exhibit 1.2.
Consider the letters involved in the word STATISTICS.
3. Refer to Exhibit1.2 above. How many "bars" would be involved if you were supposed to construct a bar graph to represent the frequency distribution of letters?
a) 6
b) 10
c) 8
d) 5
4 Refer to Exhibit 1.2 above. What is the relative frequency of letter I?
a) 2
b) 0.2
c) 0.02
d) 0.4
5. Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is
a. 20
b. 16
c. 4
d. 2
6. Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The expected value of this distribution is
a. 0.50
b. 0.30
c. 100
d. 50
7. A small company has ten employees with a mean annual salary of $75,000. The company is planning to expand its activities by hiring an administrative assistant and a consultant with annual salaries of $45,000 and $95,000, respectively. What will the mean annual employee salary be if the company expands its workforce as planned?
a) $17,916.67 b) $71,666.67 c) $74,166.67 d) $21,500
Problem
8. The following frequency distribution shows the yearly tuitions (in $1,000s) of a sample of private colleges.
Yearly
Tuition Frequency
12 - 16 5
17 - 21 4
22 - 26 3
27 - 31 2
The mean yearly tuition is:
a) $19,714.29 b) $1,971.40 c) $2000.00 b) $2,000.00
Exhibit 1-3
AMR is a computer consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
Number of
New Clients Probability
0 0.05
1 0.10
2 0.15
3 0.35
4 0.20
5 0.10
6 0.05
9. Refer to Exhibit 1-3. The variance is
a. 1.431
b. 2.047
c. 3.05
d. 21
10. If a population data set is normally distributed, what is the proportion of measurements you would expect to fall within μ ± σ?
a) 100% b) 95% c) 50% d) 68%
11. A bottling company needs to produce bottles that will hold 8 ounces of liquid for a local brewery. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 64 bottles and finds the average amount of liquid held by the 64 bottles is 7.9145 ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test turned out to be 0.0436. State the proper conclusion.
a) At α = 0.035, accept the null hypothesis.
b) At α = 0.05, reject the null hypothesis.
c) At α = 0.085, fail to reject the null hypothesis.
d) At α = 0.025, reject the null hypothesis.
Exhibit 1-4
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
12. Refer to Exhibit 1-4 above. What percentage of items will weigh at least 11.7 ounces?
a. 46.78%
b. 96.78%
c. 3.22%
d. 53.22%
13. For a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is
a. 0.4000
b. 0.0146
c. 0.0400
d. 0.5000
Exhibit 1-5
y = 28.886x + 296.52
R2 = 0.3244
0
500
1000
1500
2000
20 25 30 35 40 45 50
Newspaper Ads in Thousands of Dollars
Sales in Thousands of
Dollars
14. Refer to Exhibit 1.5 above, use the above line to predict the sales if the amount of newspaper ads is $42,000.
a) $1,418,321
b) $1,509,732
c) $1,616,789
d) $1,943,345
15. Suppose Stat I students' ages follow a skewed right distribution with a mean of 24 years old and a standard deviation of 2 years old. If we randomly sampled 150 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?
a) The mean of the sampling distribution is approximately 24 years old.
b) The standard deviation of the sampling distribution is equal to 2 years old.
c) The shape of the sampling distribution is approximately normal.
d) None of the above statements are correct.
Exhibit 1.6
HYPOTHESIS: VARIANCE X = x
X = gpa
SAMPLE MEAN OF X = 3.2854
SAMPLE VARIANCE OF X = .22000
SAMPLE SIZE OF X = 243
HYPOTHESIZED VALUE (x) = 3.4
VARIANCE X - x = -.1146
z = -3.80870
16 Find za/2 for α = 0.01.
a) 2.33
b) 1.645
c) 1.96
d) 2.575
Exhibit 1.7.
A statistical experiment involves flipping a coin that is much thicker than a regular coin of the same diameter. When flipped, the probability for the thick coin to come to rest on its edge is 4 percent; otherwise, it is a "fair coin" in the sense that we can get heads or tails with equal probabilities.
17 Refer to Exhibit 1.7 above. What is the total number of possible outcomes comprising the sample space for the statistical experiment?
a) 1 b) 2 c) 3 d) 4
18 Refer to Exhibit 1.7 above. What is the probability of getting heads when conducting the statistical experiment?
a) 0.54 b) 0.33 c) 0.46 d) 0.48
19. Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.9382?
a. 1.8
b. 1.54
c. 2.1
d. 1.77
20. High temperatures in a certain city for the month of August follow a uniform distribution over the interval 145o F to 165o F What is the probability that a randomly selected August day has a high temperature that exceeded 150o F?
a) .75.
b) .25
c) .05
d) .025
21. If a hypothesis test were conducted using α = 0.10, for which of the following p-values would the null hypothesis be rejected.
a) 0.15 b) 0.110 c) 0.090 d) 0.105
22. Suppose you are interested in conducting the statistical test of H0: u = 255 against Ha : u > 255, and you have decided to use the following decision rule: Reject H0 if the sample mean of a random sample of 81 items is more than 270. Assume that the standard deviation of the population is 63. Express the decision rule in terms of z.
a) z = 2.14 b) z < 2.14 c) z > 2.14 d) z ≠ 2.14
Solve the Problem
23. Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for tomatoes that is approximately normally distributed with a mean equal to 135 tomatoes per day and a standard deviation equal to 30 tomatoes per day. How many tomatoes must be available on any given day so that there is only a 1.5% chance that all tomatoes will be sold?
a) 200 b) 187 c) 160 d) 130
24. Given H0: μ = 25, Ha: μ ≠ 25, and P = 0.041. Do you reject or fail to reject H0 at the 0.01 level of significance?
a) not sufficient information to decide
b) reject H0
c) fail to reject H0
d) fail to accept Ha
25. A bakery has determined that the number of loaves of its white bread demanded daily has a normal distribution with a mean 7200 loaves and a standard deviation of 300 loaves. Based on cost considerations,the company has decided that its best strategy is to produce a sufficient number of loaves so that it will be fully supplied on 94% of all days. How many loaves of bread should the company produce?
a) 4678 b) 7667 c) 6800 d) 7130
26. Referring to 29, onwhat percentage of days will the company be left with more than 500 loaves of unsold bread?
a) 42.67% b) 45.62% c) 54% d) 12%
TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.
Answer the question True or False.
27. If A and B are independent events, then A and B are mutually exclusive also.
28. A Type I error occurs when we accept a false null hypothesis.
29. The binomial distribution can be used to model the number of rare events that occur over a given time period.
30. One drawback of pie charts, dot plots, stem-and-leaf displays and histograms is that no measure of reliability can be attached to a graph.