The GPA of graduating engineering students in the fictitious Kingdom of Statistans approximately normally distributed with a mean of 3.1 and a standard deviation of 0.2. The starting salary in Statistan is decided by the central government to be exactly $35K + $2.5K times the square of the GPA.
(a) What GPAs and salaries do the top 20% of graduating students have?
(b) What are the expected value and standard dev. of the starting salary?
(c) What’s the ranking of a graduating student who has a starting salary of $58K, i.e., what fraction of students have a higher starting salary?
In: Statistics and Probability
Students may choose between a 3-semester-hour physics course without labs and a 4-semester-hour course with labs. The final written examination is the same for each section. If 12 students in the section with labs made an average grade of 84 with a standard deviation of 4, and 18 students in the section without labs made an average grade of 77 with a standard deviation of 6, find a 99% confidence interval for the difference between the average grades for the two courses. Assume the populations to be approximately normally distributed with equal variances.
In: Statistics and Probability
Students may choose between a 3-semester-hour physics course without labs and a 4-semester-hour course with labs. The final written examination is the same for each section. If 12 students in the section with labs made an average grade of 84 with a standard deviation of 4, and 18 students in the section without labs made an average grade of 77 with a standard deviation of 6, find a 99% confidence interval for the difference between the average grades for the two courses. Assume the populations to be approximately normally distributed with equal variances.
In: Statistics and Probability
The school paper claims that 35% of students have credit card debt. But one thinks it’s more. simple random sample “196” students and “78,” say that they have credit card debt.
Is there sufficient evidence at the 5% significance level (α = .05) to indicate that the percent of students with credit card debt is more than 35%
Show all work (or explain what is plug into the calculator). Use specific wording.
Ho:
Ha:
Test statistic:
p-value:
Statistical conclusion:
Conclusion in plain English:
In: Statistics and Probability
Researchers are investigating how eye color affects trustworthiness. In their experiment, the researchers took photographs of 80 students, 40 of whom had brown eyes, and 40 of whom had blue eyes. They then recruited 105 participants, who judged each of the photographs on a 10 points trustworthiness scale (1pt=very untrustworthy, 10pts=very trustworthy). The mean score for brown-eyed students was 5.55, with a standard deviation of 1.68. For blue-eyed students the mean score was 4.62, with a standard deviation of 1.53.
Find the 95% confidence interval
In: Statistics and Probability
Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence to show that this is not true at her university. A random sample of 32 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 32 students studied each week was 19.1 hours. The sample standard deviation of 4.2 hours.
Find the p-value.
round to four decimal points
In: Statistics and Probability
Problem 4: In a sample of 1000 Yuba College students, it was
found that they consumed on
average 23 grams of sugar with a standard deviation of 4 grams and
that 230 planned to transfer
to Chico State.
a) (7 points) Can we conclude with 99% confidence that Yuba College
students consume on
average over 20 grams of sugar? Use the rejection region
approach.
(7 points) Can we conclude with 99% confidence that under 25% of
Yuba College students
plan to transfer to Chico State? Use the p-value approach.
In: Statistics and Probability
For each example, state whether the one-sample, two-independent-sample, or related-samples t-test is most appropriate. If it is a related-samples t-test, indicate whether the test is a repeated-measures design or a matched-pairs design:
A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year.
In: Statistics and Probability
In a study conducted to determine the role that sleep disorders play in academic performance, researcher Jane Gaultney conducted a survey of 1845 college students to determine if they had a sleep disorder (such as narcolepsy, insomnia, or restless leg syndrome). Of the 503 students with a sleep disorder, the mean grade point average was 2.65 with a standard deviation of 0.87. Of the 1342 students without a sleep disorder, the mean grade point average was 2.82 with a standard deviation of 0.83. Is there evidence to suggest sleep disorders adversely affect one’s GPA at the a = 0.05 level of significance?
In: Statistics and Probability
Assume that in a statistics class 48% of the students are in third year. Further, 49% of the students in third year are Male, and 53% of the students in a year other than third are Female.
A. If a student is randomly selected, what is the probability she is Female and is in third year?
B. If a student is randomly selected, what is the probability he is Male but not in third year?
C. If a student is randomly selected, what is the probability that he is Male?
D. Are the events Male and not in third year mutually exclusive? Explain.
E. Are the events Female and third year independent? Explain.
In: Statistics and Probability