Question 1:
A fitness trainer claims that high intensity power training decreases the body fat percentages of females. The table shows the body fat percentages of 7 females before and after 10 weeks of high intensity power training. At alpha = 0.05, is there enough evidence to support the trainer's claim?
|
Female
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
Body Fat % (before)
|
26.1
|
24.6
|
28.4
|
26.8
|
25.2
|
27.2
|
22.5
|
|
Body Fat % (after)
|
23.1
|
21.6
|
25.4
|
24.8
|
25.4
|
22.2
|
23.5
|
a) State the null and alternate hypothesis.
b) State what statistical test you used
c) State the p-value
d) State you conclusion
Question 2:
A real estate agency says that the mean home sales price in Spring, Texas, is the same as in Austin, Texas. The mean home sales price for 25 homes in Spring is $124,329. Assume the population standard deviation is $25,870. The mean home sales price for 25 homes in Austin is $110,483. Assume the population standard deviation is $27,000. At the alpha = 0.01, is there enough evidence to reject the agency's claim?
a) State the null and alternate hypothesis.
b) State what statistical test you are using.
c) State the P-value
d) State your conclusion.
Question 3:
In a survey of 350 drivers from the South, 288 wear a seat belt. In a survey of 300 drivers from the East, 281 wear a seat belt. At alpha = 0.10, can you support the claim that the proportion of drivers who wear seat belts in the South is less than the proportion of drivers who wear seat belts in the East?
a) State the null and alternate hypotheses.
b) State what statistical test you are using.
c) State the P-value
d) State your conclusion.
Question 4:
A pet association claims that the mean annual cost of food for dogs and cats are the same. The results for samples of the two types of pets are shown below. At alpha = 0.10, can you reject the pet association's claim?
|
Dogs
|
Cats
|
|
sample mean: $239
|
sample mean: $203
|
|
sample standard deviation: $32
|
sample standard deviation: $22
|
|
sample size: 16
|
sample size: 15
|
a) State the null and alternate hypotheses.
b) State the statistical test you are using.
c) State the P-value
d) State your conclusion.
Question 5:
The following table shows the average annual salary (in thousands of dollars) for public school counselors and librarians for 12 years:
|
Counselors, x
|
Librarians, y
|
|
50
|
49
|
|
50
|
48.7
|
|
51.7
|
49.6
|
|
52.3
|
50.4
|
|
52.5
|
50.7
|
|
53.7
|
53.3
|
|
55.9
|
54.9
|
|
57.6
|
56.9
|
|
58.8
|
58
|
|
60.1
|
59.5
|
|
60.2
|
59.1
|
a) Construct a scatter plot for the data.
b) Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation?
c) Calculate the correlation coefficient r and interpret the results.
d) Find the equation of the regression line for the data.
e) Use the regression line you found in part 9 to predict the average annual salary of a public school librarian (y) when the average annual salary of a public school counselor is $55,625.
Question 6:
A statistics professor wants to determine how students' final grades are related to the midterm exam grades and number of classes missed. The professor selects 10 students and obtains the data shown in the table:
|
Student
|
Final Grade, y
|
Midterm exam
|
Classes missed
|
|
1
|
81
|
74
|
1
|
|
2
|
91
|
81
|
0
|
|
3
|
85
|
90
|
3
|
|
4
|
78
|
82
|
3
|
|
5
|
60
|
60
|
7
|
|
6
|
92
|
92
|
5
|
|
7
|
60
|
62
|
6
|
|
8
|
82
|
80
|
2
|
|
9
|
88
|
90
|
0
|
|
10
|
99
|
98
|
1
|
a) Calculate the regression line.
b) Predict the final grade of a student who scores a 75 on the midterm and missed 2 days of class.
Question 7:
The table shows the results of a random sample of public elementary and secondary school teachers by gender and years of full-time teaching experience. At alpha level 0.01, can you conclude that gender is related to the years of full-time teaching experience?
|
Gender
|
Less than 3 years
|
3 - 9 years
|
10 - 20 years
|
20 year or more
|
|
Male
|
430
|
350
|
280
|
270
|
|
Female
|
330
|
800
|
670
|
650
|
a) State the null and alternate hypotheses.
b) State the P-value
c) State your conclusion.
Question 8:
A researcher claims that the number of different-colored candies in bags of peanut M&Ms is uniformly distributed. To test this claim, you randomly select a bag that contains 200 peanut M&Ms. The results are shown below. Using alpha = 0.05, test the researcher's claim.
|
Color
|
Count
|
|
Red
|
20
|
|
Green
|
30
|
|
Yellow
|
12
|
|
Blue
|
38
|
a) State the null and alternate hypotheses.
b) State the P-value
c) State your conclusion.