A fair red die and a fair green die are rolled.
(a) What is the probability that the sum of the numbers is even?
(b) What is the probability that the number on the red die is more than the number on the green die?
(c) What is the probability that the number on the red die is twice the number on the green die?
(d) What is the probability that the number on the red die is different from the number on the green die?
In: Statistics and Probability
In: Operations Management
In: Psychology
Assignment Question(s):(Marks 5)
In: Accounting
A study examined parental influence on teenagers' decisions to smoke. A group of students who had never smoked were questioned about their parents' attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that, among the
284
students who indicated that their parents disapproved of kids smoking,
64
had become established smokers. Among the
30
students who initially said their parents were lenient about smoking,
12
became smokers. Do these data provide strong evidence that parental attitude influences teenagers' decisions about smoking? Complete parts a through f.
a) What kind of design did the researchers use?
A retrospective observational study
An experiment
A prospective observational study
b) Write the appropriate hypotheses. Let
p1
be the proportion of teenagers whose parents had indicated disapproval of smoking for them who became smokers themselves. Let
p2
be the proportion of teenagers whose parents had expressed leniency toward smoking for them who became smokers themselves. Choose the correct answer below.
A.
H0:
p1minus
p2not equals
0
HA:
p1minus
p2equals
0
B.
H0:
p1minus
p2equals
0
HA:
p1minus
p2not equals
0
C.
H0:
p1minus
p2equals
0
HA:
p1minus
p2greater than
0
D.
H0:
p1minus
p2greater than
0
HA:
p1minus
p2equals
0
c) Are the assumptions and conditions necessary for inference satisfied?
A.
Yes, all of the assumptions and conditions are satisfied.
B.
No, because the randomization condition is not satisfied.
C.
No, because the 10% condition is not satisfied.
D.
No, because the success/failure condition is not satisfied.
E.
No, because the independent groups assumption is not satisfied.
d) Test the hypothesis and state your conclusion.
Determine the test statistic.
zequals
nothing
(Round to two decimal places as needed.)
Find the P-value.
Pequals
nothing
(Round to four decimal places as needed.)
State your conclusion. Use a significance level of
alpha
equals0.05
.
Choose the correct answer below.
A.
Reject
the null hypothesis. There
is
sufficient evidence that parental attitude influences teenagers' decisions about smoking.
B.
Do not reject
the null hypothesis. There
is not
sufficient evidence that parental attitude influences teenagers' decisions about smoking.
C.
Do not reject
the null hypothesis. There
is
sufficient evidence that parental attitude influences teenagers' decisions about smoking.
D.
Reject
the null hypothesis. There
is not
sufficient evidence that parental attitude influences teenagers' decisions about smoking.
e) Explain in this context what your P-value means. Choose the correct answer below.
A.
If there is no difference in the proportions, there is about a (100P)% chance of seeing the observed difference or larger by natural sampling variation.
B.
There is about a (100P)% chance that there is a difference in the proportions.
C.
There is about a (100P)% chance that there is no difference in the proportions.
D.
If the observed difference is the true difference, then there is about a (100P)% chance that there is no difference in the proportions.
f) If that conclusion is actually wrong, which type of error did you commit?
Type
Upper I
error
Type
II
error
In: Statistics and Probability
Question 1
What benefits does a company stand to gain for listing on the
Ghana Stock Exchange?
Explain why many companies are not listed in spite of the potential
benefits stated above.
Question 2
You have been appointed the portfolio manager of a GHS 1.5 billion
pension fund recently established. The fund is required to maintain
40% of its portfolio in Stock Exchange listed financial
stocks.
a) Select two financial sector stocks in your proposal to the
fund’s board of trustees. Justify your selection using at least
one-year market information.
b) A member of the board of trustees has argued for the use of a
stock index in the exercise.
i. State and describe an index on the local bourse that you would
use for this purpose.
ii. Assess the use of market indices in portfolio management.
In: Finance
STRAIGHT FROM THE BOOK
Roulette In the casino game of roulette there is a wheel
with 19 black slots, 19 red slots, and 2 green slots. In the game,
a ball is rolled around a spinning wheel and it lands in one of the
slots. It is assumed that each slot has the same probability of
getting the ball. This results in the table of probabilities
below.
Fair Table Probabilities
| black | red | green | |
| Probability | 19/40 | 19/40 | 2/40 |
You watch the game at a particular table for 130 rounds and count
the number of black, red, and green results. Your observations are
summarized in the table below.
Outcomes (n = 130)
| black | red | green | |
| Counts | 48 | 73 | 9 |
The Test: Test the claim that this roulette table
is not fair. That is, test the claim that the distribution of
colors for all spins of this wheel does not fit the expected
distribution from a fair table. Test this claim at the 0.01
significance level.
(a) What is the null hypothesis for this test?
H0: The probabilities are not all equal to 1/3.H0: p1 = 19/40, p2 = 19/40, and p3 = 2/40. H0: p1 = p2 = p3 = 1/3H0: The probabilities associated with this table do not fit those associated with a fair table.
(b) The table below is used to calculate the test statistic.
Complete the missing cells.
Round your answers to the same number of decimal places as
other entries for that column.
| Observed | Assumed | Expected | |||||
| i | Color | Frequency (Oi) | Probability (pi) | Frequency Ei |
|
||
| 1 | black | 0.475 | 61.75 | 3.062 | |||
| 2 | red | 73 | |||||
| 3 | green | 9 | 0.050 | 6.50 | 0.962 | ||
| Σ | n = 130 | χ2 = | |||||
(c) What is the value for the degrees of freedom?
(d) What is the critical value of χ2?
Use the answer found in the
χ2-table or round to 3 decimal
places.
tα =
(e) What is the conclusion regarding the null hypothesis?
reject H0
fail to reject H0
(f) Choose the appropriate concluding statement.
We have proven that this table is fair.
The results of this sample suggest the table is not fair.
There is not enough data to conclude that this table is not fair.
In: Statistics and Probability
Explain what is scientific about the study of evolution. ( HintThink about the definition of evolution and how you would apply the steps of the scientific method .)
In: Other
A snack-size bag of M&Ms candies is opened. Inside, there are 12 red candies, 12 blue, 7 green, 13 brown, 3 orange, and 10 yellow. Three candies are pulled from the bag in succession, without replacement. Determine the probability of the following. (Enter your probabilities as fractions.)
-The first candy drawn is red.
-The second candy drawn is red, given that the first candy drawn is red.
-The third candy drawn is green, given that the first two candies drawn are red.
-The first two candies drawn are red and the third is green.
**please show work
In: Statistics and Probability
A bag of 30 tulip bulbs contains 13 red tulip bulbs, 10 yellow tulip bulbs, and 7 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag.
(a) What is the probability that the two randomly selected tulip bulbs are both red?
(b) What is the probability that the first bulb selected is red and the second yellow?
(c) What is the probability that the first bulb selected is yellow and the second red?
(d) What is the probability that one bulb is red and the other yellow?
In: Statistics and Probability