In: Statistics and Probability
1. A statistics professor classifies his students according to their grade point average (GPA) and their class rank. GPA is on a 0.0 – 4.0 scale, and class rank is defined as the lower class (year 1 and year 2) and the upper class (year 3 and year 4). One student is selected at random.
| GPA | ||||
| Under 20 | 2.0 -3.0 | over 3.0 | ||
| Lower Class (Year 1 and 2) | 0.05 | 0.20 | 0.10 | 0.35 |
| Upper Class (Year 3 and 4) | 0.10 | 0.35 | 0.20 | 0.65 |
| 0.15 | 0.55 | 0.30 | 1 | |
a. Given that the student selected is in the upper class (year 3 and 4), what is the probability that her GPA over 3.0?
b. What is the probability that the student is in the upper class (year 3 and 4) or having a GPA over 3.0?
c. Are being in the upper class (year 3 and 4) and having a GPA over 3.0 independent? Prove statistically.
d. Are being in the upper class (year 3 and 4) and having a GPA over 3.0 mutually exclusive? Prove statistically.
In: Statistics and Probability
In: Statistics and Probability
In: Statistics and Probability
A probability and statistics professor surveyed 11 students in her class, asking them questions about their study strategy. The number of hours studied and the grade for the course test are in the table below:
|
Hours Studied (X) |
11 |
99 |
22 |
44 |
99 |
11 |
88 |
1010 |
66 |
99 |
22 |
|
|
Test Grade (Y) |
46 |
91 |
57 |
71 |
90 |
52 |
81 |
98 |
82 |
94 |
64 |
1.The correlation coefficient is....
he correlation coefficient in part a. suggests that the relationship between Hours Studied and Test Grade is:
A.
negative and strong
B.
positive and strong
C.
negative and weak
D.
positive and weak
In: Statistics and Probability
In a secondary school, there are 400 male students and 600 female students. 50% of the male students and 55% of the female students are in senior secondary curriculum, the others are in junior secondary curriculum. The school had appointed 8% of senior male students and 10% of senior female students to be the student leaders. No junior secondary student can be student leader.
(a) If a student is selected at random in the school, find the probability that
(i) the student is a senior student.
(ii) the student is a female student leader.
(b) Suppose a student is selected and known to be NOT a student leader, what is the probability that
(i) the student is a male student.
(ii) the student is a senior female student.
In: Statistics and Probability
Independent random samples of n1 = 800 and n2 = 610 observations were selected from binomial populations 1 and 2, and x1 = 336 and x2 = 378 successes were observed.
(a) Find a 90% confidence interval for the difference (p1 − p2) in the two population proportions. (Round your answers to three decimal places.)
_______ to _______/
(b) What assumptions must you make for the confidence interval to be valid? (Select all that apply.)
independent random samples
symmetrical distributions for both populations
n1 + n2 > 1,000
np̂ > 5 for samples from both populationsnq̂ > 5 for samples from both populations
(c) Can you conclude that there is a difference in the population proportions based on the confidence interval found in part (a)?
a. Yes. Since zero is not contained in the confidence interval, the two population proportions are likely to be different.
b. No. Since zero is not contained in the confidence interval, the two population proportions are likely to be equal.
c. No. Since zero is contained in the confidence interval, the two population proportions are likely to be equal.
d. Yes. Since zero is contained in the confidence interval, the two population proportions are likely to be different.
e. Nothing can be determined about the difference between the two population proportions.
In: Statistics and Probability
The weights of a certain dog breed are approximately normally
distributed with a mean of 52 pounds, and a standard deviation of
6.7 pounds. Answer the following questions. Write your answers in
percent form. Round your answers to the nearest tenth of a
percent.
a) Find the percentage of dogs of this breed that weigh less than
52 pounds.
b) Find the percentage of dogs of this breed that weigh less than
47 pounds.
c) Find the percentage of dogs of this breed that weigh more than
47 pounds.
In: Statistics and Probability
| Individual | Television | Radio |
| 1 | 22 | 25 |
| 2 | 8 | 10 |
| 3 | 22 | 21 |
| 4 | 22 | 18 |
| 5 | 25 | 29 |
| 6 | 13 | 10 |
| 7 | 29 | 10 |
| 8 | 26 | 25 |
| 9 | 33 | 21 |
| 10 | 16 | 15 |
| 11 | 10 | 33 |
| 12 | 30 | 12 |
| 13 | 40 | 33 |
| 14 | 16 | 38 |
| 15 | 41 | 30 |
| In recent years, a growing array of entertainment options competes for consumer time. By 2004, cable television and radio surpassed broadcast television, recorded music, and the daily newspaper to become the two entertainment media with the greatest usage (The Wall Street Journal, January 26, 2004). Researchers used a sample of 15 individuals and collected data on the hours per week spent watching cable television and hours per week spent listening to the radio. |
| a. Use a .05 level of significance and test for a difference between the population mean usage for cable television and radio. What is the p-value? |
| b. What is the sample mean number of hours per week spent watching cable television? What is the sample mean number of hours per week spent listening to radio? Which medium has the greater usage? |
In: Statistics and Probability
what is histogram? How would it be useful in interpreting the data for projectile experiment?
In: Statistics and Probability
The logistics company wants to know if the time it takes to receive shipments is the same or different for two shipping companies. A random sample of delivery times is selected for each of the two shipping firms.
The null and alternative hypotheses are:
?0: (?1−?2)=0
??: (?1−?2)≠0
A 0.10 significance level is chosen for this two-tailed test.
The samples are selected, and the results are:
?1 = 14.8 ???? ?1 = 4.6 ???? ?1 = 35
?2 = 17.4 ???? ?2 = 4.9 ???? ?2 = 47
In: Statistics and Probability
Coin 1 comes up heads with probability 0.6 and coin 2 with probability 0.5. A coin is continually flipped until it comes up tails, at which time that coin is put aside and we start flipping the other one. (a) What proportion of flips use coin 1? (b) If we start the process with coin 1 what is the probability that coin 2 is used on the fifth flip? (c) What proportion of flips land heads?
In: Statistics and Probability
In: Statistics and Probability
A research company is interested in determining the true proportion of Americans that work remotely. In a random sample of 200 individuals, 4.5% of them work remotely. Find a 90% confidence interval for the true proportion of Americans that work remotely.
In: Statistics and Probability
Perform the appropriate statistical procedure to determine if there is a difference in the amount of caffeine consumed based on level of stress and gender.
| Gender | CoffeeConsumption | Stress |
| 1 | 5 | 1 |
| 1 | 6 | 3 |
| 2 | 7 | 3 |
| 1 | 7 | 2 |
| 1 | 5 | 3 |
| 1 | 6 | 1 |
| 1 | 8 | 2 |
| 1 | 8 | 2 |
| 2 | 9 | 1 |
| 2 | 8 | 1 |
| 2 | 9 | 1 |
| 2 | 7 | 2 |
| 2 | 4 | 1 |
| 2 | 3 | 1 |
| 1 | 0 | 1 |
| 2 | 4 | 2 |
| 1 | 5 | 1 |
| 2 | 6 | 2 |
| 1 | 2 | 2 |
| 1 | 4 | 3 |
| 1 | 5 | 3 |
| 2 | 5 | 3 |
| 1 | 4 | 2 |
| 1 | 3 | 2 |
| 1 | 7 | 3 |
| 2 | 8 | 2 |
| 1 | 9 | 2 |
| 1 | 11 | 1 |
| 1 | 2 | 2 |
| 1 | 3 | 1 |
Note.
Gender: 1 Male, 2 Female
Stress: 1 Low, 2 Moderate, 3 High
In: Statistics and Probability