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?

 

Answer. 30, 480. 6-5

 

 

 

 

 

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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