# Project #1191 - stats homework

Math 160 Statistics Extra Work

Optional. Each counts 1 point for the final grade

1. At a faculty meeting, there were 8 full professors, 6 associate professors, 7 assistant

professors and 13 instructors. If 5 people are selected at random to attend a conference, find

the probability at least two are full professors.  Answer: 0.33. 4-4

2. In a survey, 65% of Americans said they own an answering machine. If 20 Americans are

selected randomly, (a) find the probabilities that at least 18 people own an answering machine

and (b) find the mean and the standard deviation the number of people owning an answering

machine. Answer: (a) 0.012. (b) 2.133. 5-4

3. An instructor gives a 1 00-point examination in which the grades are normally distributed. The

mean is 70 and the standard deviation is 9. There are 12% A's, 23% B's, 42% C's, 18% D's,

and 5% F's. Find the scores that divide the distribution into those categories. Answer: 80.58,

73.47, 63.35, 55.20. 6-4

4. The standard deviation of the average waiting time to see a doctor for non-threatening

problems in the emergency room at an urban hospital is 33 minutes. At a second hospital the

standard deviation is 29 minutes. If 66 patients were used in the first hospital sample and 125

patients were used in the second hospital sample, can we conclude that the second hospital

has a smaller standard deviation? Use a = 0. 01 . Answer. No. 9-3

5. Find n for the equations: (a) 2nP3 = 7 ( n+1 P3 ). (b) [ nPs + 2 ( nP 4 ) ] I [ 3 ( nP3 ) ] = 4. Answer:

(a)11.(b)6. 4-5

6. The standard deviation of a variable is 20. If a sample of 120 individuals is selected, compute

the standard error of the mean. What size sample is necessary to double the standard error of

the mean? What size sample is needed to cut the standard error of the mean in half?

7. The average time it takes a person in a one-person canoe to complete a certain river course is

50 minutes. Because of rapid currents in the spring, a group of 12 people traverse the course

in 46 minutes. The standard deviation, known from previous trips, is 8 minutes. Test the

claim that this group's time was different because of the strong currents. Use a= 0.05. Find

the 95% confidence level of the mean. Does the confidence interval interpretation agree with

the results of the hypothesis test? Explain. Assume that the variable is normally distributed.

Answer. No enough evidence to support the claim. Cl = ( 41.49, 50.51 ). Hypothetical value=

50 belongs to Cl and not reject H0 in the test problem. 8-7

8. In a sample of 80 high school seniors, 12 had their own cars. In a sample of 95 college

freshmen, 25 had their own cars. (a) At a= 0.05, can it be concluded that a higher proportion

of college freshmen have their own cars? Use the P-value method. (b) Estimate the true

difference in the two proportions with 95% confidence. Answer. (a) Support the claim. (b) Cl

= ( -0.2306, 0.0046 ). 9-6

9. Are some fast-food restaurants healthier than others? The number of grams of fat in a regular

serving of French fries for a random sample of restaurants is: { 15, 13, 15, 22, 13, 21, 10, 21,

10, 17, 11, 17, 15, 18, 24, 18 }. Is there sufficient evidence to conclude that the standard

deviation exceeds 4 grams of fat? Use a = 0.1. Answer. No sufficient evidence to support

the claim. 8-6

10. Females and males alike from the general adult population volunteer an average of 4.5 hours

per week. A random sample of 13 female college students and 9 male college students

indicated these results shown below concerning the amount of time spent in volunteer

service per week. At the 0.05 level of significance, is there sufficient evidence to conclude

that a difference exists between the mean number of volunteer hours per week for male and

female college students?

Men                             Women

Sample mean                  2.6                            3.9

Sample variance          2.3                               3.6

Sample size                 9                                  13

Answer: No enough evidence to support the claim. 9-4

 Subject Mathematics Due By (Pacific Time) 11/14/2012 04:00 am
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