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Textbook by: Kathy Chu, Ph.D.. E-mail the author

# Review

Summary: 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.

## Exercise 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.

D

## Exercise 2

Construct a histogram of the IPO data (see Table of Contents, 14. Appendix, Data Sets). Use 5 intervals.

### Solution

No solution provided. There are several ways in which the histogram could be constructed.

The next three exercises 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

Complete the cumulative relative frequency column.

## Exercise 3

Calculate the sample mean (a), the sample standard deviation (b) and the percent of the estimates that fall at or below 4 (c).

• a. 2.8
• b. 1.48
• c. 90%

## Exercise 4

Calculate the median, M, the first quartile, Q1, the third quartile, Q3. Then construct a boxplot of the data.

### 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 5

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

### Solution

1 and 4

The next three questions refer to the following table: Seventy 5th and 6th graders were asked their favorite dinner.

Table 2
Pizza Hamburgers Spaghetti Fried shrimp
5th grader 15 6 9 0
6th grader 15 7 10 8

## Exercise 6

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"} } } } {}

D

## Exercise 7

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

C

## Exercise 8

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"} } } } {}

A

## Exercise 9

A sample of convenience is a random sample.

• A. true
• B. false

B

## Exercise 10

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

• A. true
• B. false

B

## Exercise 11

You should always throw out any data that are outliers.

• A. true
• B. false

B

## Exercise 12

Lee bakes pies for a small restaurant in Felton, CA. She generally bakes 20 pies in a day, on the average. Of interest is the num.ber of pies she bakes each day

• 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

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

## Exercise 13

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 mean grams of fat per serving of Italian salad dressing sold in supermarkets.

### Solution

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

## Exercise 14

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

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

### Solution

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

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