Hypothesis Testing of Single Mean and Single Proportion: Review
1.6
2008/06/06 17:47:13 GMT-5
2008/08/15 12:07:18.649 GMT-5
Barbara
Illowsky
illowskybarbara@deanza.edu
Susan
Dean
deansusan@deanza.edu
Connexions
cnx@cnx.org
elementary
statistics
This module provides an overview of Hypothesis Testing of Single Mean and Single Proportion as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
1. Rebecca and Matt are 14 year old twins. Matt’s height is 2 standard deviations below the mean for 14 year old boys’ height. Rebecca’s height is 0.10 standard deviations above the mean for 14 year old girls’ height. Interpret this.
- AMatt is 2.1 inches shorter than Rebecca
- BRebecca is very tall compared to other 14 year old girls.
- CRebecca is taller than Matt.
- DMatt is shorter than the average 14 year old boy.
D
2. Construct a histogram of the IPO data (see Table of Contents). Use 5 intervals.
The next six questions refer to the following information: Ninety homeowners were asked the number of estimates they obtained before having their homes fumigated.
X size 12{X} {} = the number of estimates.
X
size 12{X} {}
Rel. Freq.
Cumulative Rel. Freq.
1
0.3
2
0.2
4
0.4
5
0.1
3. Calculate the frequencies.
4. Complete the cumulative relative frequency column. What percent of the estimates fell at or below 4?
5. Calculate the sample mean (a) and sample standard deviation (b).
- a2.8
- b 1.48
6. Calculate the median, M, the first quartile, Q1, the third quartile, Q3.
M
=
3
size 12{M=3} {}
;
Q1
=
1
size 12{Q1=1} {}
;
Q3
=
4
size 12{Q3=4} {}
7. The middle 50% of the data are between _____ and _____.
1 and 4
8. Construct a boxplot of the data.
The next three questions refer to the following table: Seventy 5th and 6th graders were asked their favorite dinner.
Pizza
Hamburgers
Spaghetti
Fried shrimp
5th grader
15
6
9
0
6th grader
15
7
10
8
9. Find the probability that one randomly chosen child is in the 6th grade and prefers fried shrimp.
- A
3270 size 12{ { { size 8{"32"} } over { size 8{"70"} } } } {}
- B
832 size 12{ { { size 8{8} } over { size 8{"32"} } } } {}
- C
88 size 12{ { { size 8{8} } over { size 8{8} } } } {}
- D
870 size 12{ { { size 8{8} } over { size 8{"70"} } } } {}
D
10. Find the probability that a child does not prefer pizza.
- A
3070 size 12{ { { size 8{"30"} } over { size 8{"70"} } } } {}
- B
3040 size 12{ { { size 8{"30"} } over { size 8{"40"} } } } {}
- C
4070 size 12{ { { size 8{"40"} } over { size 8{"70"} } } } {}
- D1
C
11. Find the probability a child is in the 5th grade given that the child prefers spaghetti.
- A
9
19
size 12{ { { size 8{9} } over { size 8{"19"} } } } {}
- B
9
70
size 12{ { { size 8{9} } over { size 8{"70"} } } } {}
- C
9
30
size 12{ { { size 8{9} } over { size 8{"30"} } } } {}
- D
19
70
size 12{ { { size 8{"19"} } over { size 8{"70"} } } } {}
A
12. A sample of convenience is a random sample.- Atrue
- Bfalse
B
13. A statistic is a number that is a property of the population.
- Atrue
- Bfalse
B
14. You should always throw out any data that are outliers.
- Atrue
- Bfalse
B
15. Lee bakes pies for a little restaurant in Felton. She generally bakes 20 pies in a day, on the average.
- aDefine the Random Variable
X size 12{X} {}.
- bState the distribution for
X size 12{X} {}.
- cFind the probability that Lee bakes more than 25 pies in any given day.
- b
P
(
20
)
size 12{P \( "20" \) } {}
- c0.1122
16. Six different brands of Italian salad dressing were randomly selected at a supermarket. The grams of fat per serving are 7, 7, 9, 6, 8, 5. Assume that the underlying distribution is normal. Calculate a 95% confidence interval for the population average grams of fat per serving of Italian salad dressing sold in supermarkets.
CI:
(
5
.
52
,
8
.
48
)
size 12{ ital "CI": \( 5 "." "52",8 "." "48" \) } {}
17. Given: uniform, exponential, normal distributions. Match each to a statement below.
- amean = median ≠ mode
- bmean > median > mode
- cmean = median = mode
- auniform
- bexponential
- cnormal