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# Hypothesis Testing of Single Mean and Single Proportion: Review Questions

Module by: Roberta Bloom. E-mail the author

Summary: Copy of Review Questions module m17013 (http://cnx.org/content/m17013/latest/) from Collaborative Statistics by Dean and Illowsky http://cnx.org/content/col10522/ , 12/18/2008 . The FORMAT only of the question numbering has been changed.

## Exercise 1: REVIEW QUESTION 1

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.

• A. Matt is 2.1 inches shorter than Rebecca
• B. Rebecca is very tall compared to other 14 year old girls.
• C. Rebecca is taller than Matt.
• D. Matt is shorter than the average 14 year old boy.

### Solution

REVIEW QUESTION 1 Solution : D

## Exercise 2: REVIEW QUESTION 2

2. Construct a histogram of the IPO data (see Appendix). 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. XX size 12{X} {} = the number of estimates.

Table 1
X X size 12{X} {} Rel. Freq. Cumulative Rel. Freq.
1 0.3
2 0.2
4 0.4
5 0.1

## Exercise 3: REVIEW QUESTION 3

Calculate the frequencies

### Solution

REVIEW QUESTION 3 Solution

Table 2
X X size 12{X} {} Frequency
1 27
2 18
4 36
5 9

## Exercise 4: REVIEW QUESTION 4

Complete the cumulative relative frequency column. What percent of the estimates fell at or below 4?

### Solution

REVIEW QUESTION 4 Solution : 90%

## Exercise 5: REVIEW QUESTION 5

5. Calculate the sample mean (a) and sample standard deviation (b).

• a. 2.8
• b. 1.48

## Exercise 6: REVIEW QUESTION 6

6. Calculate the median, M, the first quartile, Q1, the third quartile, Q3.

### Solution

REVIEW QUESTION 6 Solution : M = 3 M = 3 size 12{M=3} {} ; Q1 = 1 Q1 = 1 size 12{Q1=1} {} ; Q3 = 4 Q3 = 4 size 12{Q3=4} {}

## Exercise 7: REVIEW QUESTION 7

7. The middle 50% of the data are between _____ and _____.

### Solution

REVIEW QUESTION 7 Solution : 1 and 4

## Exercise 8: REVIEW QUESTION 8

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.

Table 3
Pizza Hamburgers Spaghetti Fried shrimp
5th grader 15 6 9 0
6th grader 15 7 10 8

## Exercise 9: REVIEW QUESTION 9

9. Find the probability that one randomly chosen child is in the 6th grade and prefers fried shrimp.

• A. 32703270 size 12{ { { size 8{"32"} } over { size 8{"70"} } } } {}
• B. 832832 size 12{ { { size 8{8} } over { size 8{"32"} } } } {}
• C. 8888 size 12{ { { size 8{8} } over { size 8{8} } } } {}
• D. 870870 size 12{ { { size 8{8} } over { size 8{"70"} } } } {}

### Solution

REVIEW QUESTION 9 Solution : D

## Exercise 10: REVIEW QUESTION 10

10. Find the probability that a child does not prefer pizza.

• A. 30703070 size 12{ { { size 8{"30"} } over { size 8{"70"} } } } {}
• B. 30403040 size 12{ { { size 8{"30"} } over { size 8{"40"} } } } {}
• C. 40704070 size 12{ { { size 8{"40"} } over { size 8{"70"} } } } {}
• D. 1

### Solution

REVIEW QUESTION 10 Solution : C

## Exercise 11: REVIEW QUESTION 11

11. Find the probability a child is in the 5th grade given that the child prefers spaghetti.

• A. 9 19 9 19 size 12{ { { size 8{9} } over { size 8{"19"} } } } {}
• B. 9 70 9 70 size 12{ { { size 8{9} } over { size 8{"70"} } } } {}
• C. 9 30 9 30 size 12{ { { size 8{9} } over { size 8{"30"} } } } {}
• D. 19 70 19 70 size 12{ { { size 8{"19"} } over { size 8{"70"} } } } {}

### Solution

REVIEW QUESTION 11 Solution : A

## Exercise 12: REVIEW QUESTION 12

12. A sample of convenience is a random sample.

• A. true
• B. false

### Solution

REVIEW QUESTION 12 Solution : B

## Exercise 13: REVIEW QUESTION 13

13. A statistic is a number that is a property of the population.

• A. true
• B. false

### Solution

REVIEW QUESTION 13 Solution : B

## Exercise 14: REVIEW QUESTION 14

14. You should always throw out any data that are outliers.

• A. true
• B. false

### Solution

REVIEW QUESTION 14 Solution : B

## Exercise 15: REVIEW QUESTION 15

15. Lee bakes pies for a little restaurant in Felton. She generally bakes 20 pies in a day, on the average.

• a. Define the Random Variable XX size 12{X} {}.
• b. State the distribution for XX size 12{X} {}.
• c. Find the probability that Lee bakes more than 25 pies in any given day.

### Solution

#### REVIEW QUESTION 15 Solution

• b. P ( 20 ) P ( 20 ) size 12{P $$"20"$$ } {}
• c. 0.1122

## Exercise 16: REVIEW QUESTION 16

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.

### Solution

REVIEW QUESTION 16 Solution : CI: ( 5 . 52 , 8 . 48 ) ( 5 . 52 , 8 . 48 ) size 12{ ital "CI": $$5 "." "52",8 "." "48"$$ } {}

## Exercise 17: REVIEW QUESTION 17

17. Given: uniform, exponential, normal distributions. Match each to a statement below.

• a. mean = median ≠ mode
• b. mean > median > mode
• c. mean = median = mode

### Solution

#### REVIEW QUESTION 17 Solution

• a. uniform
• b. exponential
• c. normal

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