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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.

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.

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

D

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

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. 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

Complete the cumulative relative frequency column.

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

  • 2.8
  • 1.48
  • 90%

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

M = 3 size 12{M=3} {} ; Q1 = 1 size 12{Q1=1} {} ; Q3 = 4 size 12{Q3=4} {}

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

1 and 4

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

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

  • 32 70 size 12{ { { size 8{"32"} } over { size 8{"70"} } } } {}
  • 8 32 size 12{ { { size 8{8} } over { size 8{"32"} } } } {}
  • 8 8 size 12{ { { size 8{8} } over { size 8{8} } } } {}
  • 8 70 size 12{ { { size 8{8} } over { size 8{"70"} } } } {}

D

Find the probability that a child does not prefer pizza.

  • 30 70 size 12{ { { size 8{"30"} } over { size 8{"70"} } } } {}
  • 30 40 size 12{ { { size 8{"30"} } over { size 8{"40"} } } } {}
  • 40 70 size 12{ { { size 8{"40"} } over { size 8{"70"} } } } {}
  • 1

C

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

  • 9 19 size 12{ { { size 8{9} } over { size 8{"19"} } } } {}
  • 9 70 size 12{ { { size 8{9} } over { size 8{"70"} } } } {}
  • 9 30 size 12{ { { size 8{9} } over { size 8{"30"} } } } {}
  • 19 70 size 12{ { { size 8{"19"} } over { size 8{"70"} } } } {}

A

A sample of convenience is a random sample.

  • true
  • false

B

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

  • true
  • false

B

You should always throw out any data that are outliers.

  • true
  • false

B

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

  • Define the Random Variable X size 12{X} {} .
  • State the distribution for X size 12{X} {} .
  • Find the probability that Lee bakes more than 25 pies in any given day.
  • P ( 20 ) size 12{P \( "20" \) } {}
  • 0.1122

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.

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

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

  • mean = median ≠ mode
  • mean>median>mode
  • mean = median = mode
  • uniform
  • exponential
  • normal
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Source:  OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
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