Question

1.5 Suppose you believe that, in general, graduates who have majored in your subject are offered higher salaries upon graduating than are graduates of other programs. Describe a statistical experiment that could help test your belief.

1.6 You are shown a coin that its owner says is fair in the sense that it will produce the same number of
heads and tails when flipped a very large number of times.

a.Describe an experiment to test this claim.

b. What is the population in your experiment?

c. What is the sample?

d. What is the parameter?
e. What is the statistic?

f. Describe briefly how statistical inference can be used to test the claim.

1.7 Suppose that in Exercise

1.6 you decide to flip the coin 100 times.

a.What conclusion would you be likely to draw if you observed 95 heads?
b. What conclusion would you be likely to draw if you observed 55 heads?
c.Do you believe that, if you flip a perfectly fair coin 100 times, you will always observe exactly 50 heads? If you answered “no,” then what numbers do you think are possible? If you answered “yes,” how many heads would you observe if you flipped the coin twice? Try flipping a coin twice and repeating this experiment 10 times and report the results.

1.8 Xr01-08 The owner of a large fleet of taxis is trying to estimate his costs for next year’s operations. One major cost is fuel purchase. To estimate fuel purchase, the owner needs to know the total distance his taxis will travel next year, the cost of a gallon of fuel, and the fuel mileage of his taxis. The owner has been provided with the first two figures (distance estimate and cost of a gallon of fuel). However, because of the high cost of gasoline, the owner has recently converted his taxis to operate on propane. He has measured and recorded the propane mileage (in miles per gallon) for 50 taxis.

a.What is the population of interest?
b. What is the parameter the owner needs?

c. What is the sample?
d. What is the statistic?

e. Describe briefly how the statistic will produce the kind of information the owner wants.

Answer 1

1.5

Question: Suppose you believe that, in general, graduates who have majored in your subject are offered higher salaries upon graduating than are graduates of other programs. Describe a statistical experiment that could help test your belief.

Form 2 independent mutually exclusive groups:

Group 1: Experimental Group: Sample size = n1 = number of graduates who have majored in your subject

Group 2: Control Group : Sample size = n2 = number of graduates who have majored in other programs.

From the data collected, obtain: 1, s1, 2, s2

H0: Null Hypothesis: (graduates who have majored in your subject are not offered higher salaries upon graduating than are graduates of other programs)

HA: Alternative Hypothesis: (graduates who have majored in your subject are offered higher salaries upon graduating than are graduates of other programs) (Claim)

From the above details, a statistical experiment that could help test your belief that graduates who have majored in your subject are offered higher salaries upon graduating than are graduates of other programs.

1.6

a. An experiment to test the claim that the coin will produce the same number of heads and tails when flipped a very large number of times:

Flip the coin for Sample Size = n, a very large number of times:

Obtain the number heads = x in the experiment.

Calculate:
Sample Proportion: = x/n

H0: Null Hypothesis: p = 0.5 (the coin will produce the same number of heads and tails when flipped a very large number of times) (Claim)

HA: Alternative Hypothesis: p 0.5 the coin will not produce the same number of heads and tails when flipped a very large number of times)

From the above details, a statistical experiment that could help test whether the coin will produce the same number of heads and tails when flipped a very large number of times)

(b) the population in your experiment = Fair coin

(c) Sample: Values of heads obtained by flipping n times.

(d) Parameter: Population proportion = p = 0.5

(e) Statistic: Sample proportion = : = x/n

(f)

H0: Null Hypothesis: p = 0.5 (the coin will produce the same number of heads and tails when flipped a very large number of times) (Claim)

HA: Alternative Hypothesis: p 0.5 the coin will not produce the same number of heads and tails when flipped a very large number of times)

Two tailed Hypothesis Test is conducted to test the claim that the coin will produce the same number of heads and tails when flipped a very large number of times.

1.6

(a)

n = 100

= 95/100 = 0.95

SE =

Test Statistic is given by:
Z = (0.95 - 0.50)/0.05

= 9.00

Take = 0.05

From Table, critical values of Z = 1.96

Since calculated value of Z is greater than critical value of Z, conclude: The coin is not fair.

(b)

n = 100

= 55/100 = 0.55

SE =

Test Statistic is given by:
Z = (0.55 - 0.50)/0.05

= 1.00

Take =0.05

From Table, critical values of Z = 1.96

Since calculated value of Z is less than critical value of Z, conclude: The coin is fair.

(c)

Question:

Do you believe that, if you flip a perfectly fair coin 100 times, you will always observe exactly 50 heads?

Answer : No

The possible numbers are got as follows:

= np = 100 X 0.5 = 50

So,

possible values are:

50 (2 X 5)

= 40 to 60

1.8

(a) the population of interest = large fleet of taxis of the owner

(b) the parameter the owner needs = propane mileage (in miles per gallon)

(c) sample: 50 taxis.

(d) the statistic: the propane mileage (in miles per gallon) for 50 taxis.

(e) One sample t test (two - tailed) will produce the kind of information the owner wants.