In the High School there is around 2500 students, 18% of the students smoke cigarettes.
A) If 2 are selected at random, use a Venn diagram with 2 circles; 1 representing the probability that the first student smokes and 1 representing the probability that the other student smokes. Determine the probability that at least 1 of them smokes cigarettes. (This would be equivalent to the probability that either the first student OR the second student smokes.)
B) Repeat the above analysis when 3 students are selected at random.
Note: These trials would be independent given the large population of students.
In: Statistics and Probability
In a situation where there are 25 students in a class (students are numbered from 1 to 25) and they each have random birthdays so every birthday has a probability of 1/365, there is an event E[a, b] where a and b is each pair of students.
1. How many possible events are there and what is the probability of each one?
2. What is the expected number of pairs of students who would share a birthday (using linearity of expectation)?
3. Would the number of pairs who share a birthday be a binomial random variable?
In: Statistics and Probability
A survey is given to 300 random SCSU students to determine their opinion of being a “Tobacco Free Campus.” Of the 300 students surveyed, 230 were in favor a tobacco free campus. Find a 95% confidence interval for the proportion of all SCSU students in favor of a tobacco free campus. Interpret the interval in part a.
Find the error bound of the interval in part a. The Dean claims that at least 70% of all students are in favor of a tobacco free campus.
Can you support the Dean’s claim at the 95% confidence level? Justify!
In: Statistics and Probability
Let us suppose that heights of Richmond students are normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches.
a. What will be the height of a student who is in the top 1%? Is this the minimum or the maximum height?
b. What is the height range of students who are between the third and fourth quintile?
c. What proportion of students are between 60 and 65 inches in height?
d. What will be the height of a student who is in the first decile? Is this the minimum or the maximum height? e. How many students are between 65.5 and 70.5 inches I height?
In: Statistics and Probability
One hundred students were given an Algebra test. A random sample of ten students was taken out of class of 800 enrolled students. The time it took each student to complete the test is recorded below.
22.2, 23.7, 16.8, 18.3, 19.7, 16.9, 17.2, 18.5, 21.0, and 19.7
a. Find the mean, variance and standard deviation for this sample of ten students
b. Construct a 95% confidence interval for the population mean time to complete this Algebra test.
c. Test if the population mean time to complete the test is 22.5 minutes.
In: Statistics and Probability
(1 point) A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 253 students was x⎯⎯⎯x¯ = 134 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σσ = 65 minutes in the population of all first-year students at this university.
Use the survey result to give a 90% confidence interval for the mean study time of all first-year students.
In: Statistics and Probability
A journal published a study of the lifestyles of visually impaired students. Using diaries, the students kept track of several variables, including number of hours of sleep obtained in a typical day. These visually impaired students had a mean of 9.06hours and a standard deviation of 2.11 hours. Assume that the distribution of the number of hours of sleep for this group of students is approximately normal. Complete parts a through c.
A. Find P(x<6)
b. Find P(8≤x≤10)
c. Find the value a for which P(x<a)= 0.3
In: Statistics and Probability
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The national health organization warns that 30% of the middle school students nationwide have been drunk. A local health agency randomly and anonymously surveys 100 of the middle school students in its city and finds that only 21 of them report having been drunk. |
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Create a 95% confidence interval for the proportion of the city's middle school students who have been drunk. |
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Is there any reason to believe that the national level of 30% is not true for the middle school students in the city? Test at 1% significance level. |
In: Statistics and Probability
A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken 5 years ago. Five years ago, a sample of 270 students showed that 120 considered themselves overweight. This year a poll of 300 students showed that 140 considered themselves overweight. At a 5% level of significance, test to see if there is any difference in the proportion of college students who consider themselves overweight between the two polls. What is your conclusion? Show all work and please make legible
In: Statistics and Probability
A study was conducted for the effects of marijuana use on college students. Memory recall was evaluated by asking students to sort items.
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Light Marijuana Users |
Heavy Marijuana Users |
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n = 64 students x = 53.3 items correctly sorted s = 3.6 items correctly sorted |
n = 65 students x = 51.3 items correctly sorted s = 4.5 items correctly sorted |
At the 5% LOS, do the data suggest test that light users correctly sort more items than heavy users?
In: Statistics and Probability