1.22         a. the frequency plots are given below. The direction of extreme is two sided.

                b. H0: The shown bag is Bag A. H1: The shown bag is Bag B.

                c. Answer may vary. One reasonable rule is to reject H0 is the selected token is < $4 or > $16.

                d. The significance level a-6/50=0.12

                e. The chance of a Type II error is b=16/50=0.32

                f.     (i)    Accept H0

(ii)    A Type II error

                g.     (i)     Reject H0

                        (ii)    A Type I error.

1.24         a. H0: The shown jar is Jar A. H1: The shown jar is Jar B.

b. No, the coins are of different sizes and weights. If we mixed up the contents of the shown jar and reached in to pick one coin, the coins that we are more likely to pick might be a quarter as it has a larger size as compared to say a dime. The larger coins may be more likely to be selected over the smaller coins. This will be referred to later in Chapter 2 as a length biased sampling method.

c. The responses are currently listed as P, N, D, and Q, but there is an ordering to them with respect to their value. So a better way to record the response would be using their worth of 1, 5, 10, or 25 cents. Correspondingly, a better picture to depict the two models for the shown jar is given below. The direction of extreme would be to the right , to the larger coin values.

1.40       a. H0: The population of all goats born to mother goats that were trained to walk on a treadmill has a mean birth weight of 1600 grams. H1: The population of all goats born to mother goats that were trained to walk on a treadmill has a mean birth weight different from 1600 grams. 

               b. The null hypothesis was supported at the 1% level.

               c. The p-value was more than 0.01. 

               d. Answer will vary. One possible p-value is 0.08.

               e. Yes, as now the p-value must be larger than 0.01 but less than or equal to 0.05. A value that will satisfy this statement on significance is 0.04.

               f. A Type II error could have been made.

Additional Problem #1

a) F

b) T
c) T
d) T

Additional Problem #2

a) F
b) F
c) F (the direction of extreme is to the right)
d) T
 

2.4a. 22.4

b. 19. No.

c. 22.5. No. No.

d.     18 and 21. The sample mean age is 19.5.

        18 and 26. The sample mean age is 22.

        20 and 27. The sample mean age is 23.5.

        20 and 21. The sample mean age is 20.5.

        20 and 26. The sample mean age is 23.

        27 and 21. The sample mean age is 24.

        27 and 26. The sample mean age is 26.5.

2.6           For a simple random sample of n=200 and the number of items that were defective=5. All we can say is that (C) the perent of defective items in the sample is 5/200=2.5%. p=5/200=0.025=2.5%

2.8a. Population: Adults U.S. residents. The sample size n=1500.

b. Population: Todayˇ¦s shipment of 1-gallon milk cartons. The sample size n=5.

c. Population: The 740 members of the local womenˇ¦s business association. The sample size n=100.

2.10         a. Statistic since the 54% is a sample percentage, not of the population.

                b. Nonresponse bias.

2.20a. 12/100

b. With the graphing calculator the selected employee are: 77,51,72,40,71,42,17,34,62,23,35,15.

    From the random table the selected employees are:

    7,5,69,76,28,33,78,70,99,98,42,80.


Additonal Problem #1
Population:  All US Senators
Size of the Population: N=100
Sample: Senators selected by the newspaper
n = 18.