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Hypothesis Testing of Single Mean and Single Proportion: Review

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

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.

Solution

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).

Solution

  • 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"} } } } {}

Solution

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

Solution

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"} } } } {}

Solution

A

Exercise 9

A sample of convenience is a random sample.

  • A. true
  • B. false

Solution

B

Exercise 10

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

  • A. true
  • B. false

Solution

B

Exercise 11

You should always throw out any data that are outliers.

  • A. true
  • B. false

Solution

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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