1. Given the following sample of 10 high temperatures from March: 55, 60, 57, 43, 59, 66, 72, 65, 59, 47.
a. Determine the mean.
b. Determine the median.
c. Determine the mode.
d. Describe the shape of the distribution.
e. Determine Q1, Q2, Q3 and IQR.
2. The contingency table shows classification of students in a Statistics class.
From NJ
From PA
GPA at least 3.0
15
5
20
GPA below 3.0
45
35
80
60
40
100
a. If a student is selected at random, what is the probability that he/she is from NJ?
b. If a student is selected at random, what is the probability that he/she has a GPA below 3.0?
c. If we know that the student is from PA, what is the probability that he/she has a GPA of at least 3.0?
d. If a student is selected at random, what is the probability that he/she is from NJ and has a GPA below 3.0.
e. If a student is selected at random, what is the probability that he/she from PA and has GPA of at least 3.0.
3. Your friend is applying for 4 jobs. The hourly pay rate for the 4 jobs are, $8, $12, $15, $20. The probability distribution below shows the probability of getting each of these jobs:
Job Pay Rate, X Probability, P(X)
8 .30
12 .20
15 .40
20 .10
a. What is the probability that your friend will get a job paying at least $15/hour?
b. What is the expected pay rate for your friend?
4. It is known that 31% of cars are considered gas hogs (i.e. they give less than 15 mpg). If we select 20 cars at random:
a. What is the probability that exactly 4 will be gas hogs?
b. What is the probability the at least 4 but not more than 7 will be gas hogs?
c. How many cars are most likely to be gas hogs?
5. You ask all 200 students at school how much money they have in their pockets. The amount ranges from $0 to $130. You determine the mean to be $56.40 with standard deviation of $8.40. You believe that the amount is normally distributed.
a. If you pick a person at random, what is the probability that he/she has at least $45?
b. What percentage of the students will have between $40 and $50 in their pockets.
c. If you pick a person at random, what is the probability that he/she has either less than $30 or more than $70.
d. Approximately how many people in the class do you expect to have at least $65?
e. We want to identify the students with top 10.5% amounts as "rich". What is the minimum dollar amount the students in this group would need in their pockets.
6. Assume that on the third exam in a calculus course, the average score over the years has been 72 with a standard deviation 12. You are currently taking the course and there are 25 students in the class?
What is the probability that the mean score for your class will be greater than 75?
What is the probability that the mean score for your class will be between 68 and 70?
7. A sample of 25 days in summer yields an average high temperature of 80 with a standard deviation of 12.
a. Give a point estimate of the true mean of the high temperature.
b. Find a 99% confidence interval for the average high temperature for the summer.
c. How big a sample do we need if we want to be 90% confident of being within 7 degrees of the population mean?
8. A sample of 100 exams yielded an average grade of 82 and standard deviation of 14. Find a 95% confidence interval for the average exam grade.
9. Heights of aliens from Mars are known to be normally distributed with a population standard deviation of 9 inches. How big a sample do we need to take if we want be 95% confident that our error will not exceed 3 inches?
10. Preliminary studies have shown that 20% of the voters might be willing to vote for Sran for President.
a. Construct a 90% confidence interval for the proportion of voters who would be willing to support Sran.
b. Before entering the race, Sran would like to conduct a poll to check his level of support. How big should be the sample be if he wants to be 95% sure that the error is no more than 2%?
11. The average weight of men joining a gym has historically been 170 pounds with a standard deviation of 27. The owner feels that the average weight has now decreased to less than 165 pounds. To support his claim, the owner conducts a sample of 25 men and finds their average to be 153. He would like to use a significance level of .05 to test his claim.
a. State the null hypothesis.
b. State the alternate hypothesis.
c. Will you use z or t distribution for this problem?
d. Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.
e. Determine the critical value.
f. Determine the rejection region.
g. Calculate the test statistic.
h. Would you accept or reject the owner's claim? Explain.
12. The average score on a certain college entrance test has been known to be 240. The dean of a university feels that this has changed. He conducts a sample of 25 students to test his claim. The sample yields an average of 232 with a standard deviation of 25. He would like to use a significance level of .10.
a. State the null hypothesis.
b. State the alternate hypothesis.
c. Will you use z or t distribution for this problem?
d. Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.
e. Determine the critical value.
f. Determine the rejection region.
g. Calculate the test statistic.
h. Would you accept or reject the dean's claim?
13. A presidential candidate states that she currently has exactly 30% of the vote. A newspaper thinks that this number is inaccurate. So it conducts a sample 500 voters and finds 175 people support the candidate. The newspaper would like to test its claim using .05 significance level.
a. State the null hypothesis.
b. State the alternate hypothesis.
c. Will you use z or t distribution for this problem?
d. Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.
e. Determine the critical value.
f. Determine the rejection region.
g. Calculate the test statistic.
h. Would you accept or reject the newspaper's claim?