<< Chapter < Page Chapter >> Page >

References

Data from the United States Census Bureau. Available online at http://www.census.gov/prod/cen2010/briefs/c2010br-02.pdf

Hinduja, Sameer. “Sexting Research and Gender Differences.” Cyberbulling Research Center, 2013. Available online at http://cyberbullying.us/blog/sexting-research-and-gender-differences/ (accessed June 17, 2013).

“Smart Phone Users, By the Numbers.” Visually, 2013. Available online at http://visual.ly/smart-phone-users-numbers (accessed June 17, 2013).

Smith, Aaron. “35% of American adults own a Smartphone.” Pew Internet, 2013. Available online at http://www.pewinternet.org/~/media/Files/Reports/2011/PIP_Smartphones.pdf (accessed June 17, 2013).

“State-Specific Prevalence of Obesity AmongAduls—Unites States, 2007.” MMWR, CDC. Available online at http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5728a1.htm (accessed June 17, 2013).

“Texas Crime Rates 1960–1012.” FBI, Uniform Crime Reports, 2013. Available online at: http://www.disastercenter.com/crime/txcrime.htm (accessed June 17, 2013).

Chapter review

A hypothesis test of two population means from independent samples where the population standard deviations are known (typically approximated with the sample standard deviations), will have these characteristics:

  • Random variable: X ¯ 1 X ¯ 2 = the difference of the means
  • Distribution: normal distribution

Formula review

Normal Distribution:
X ¯ 1 X ¯ 2 N [ μ 1 μ 2 , ( σ 1 ) 2 n 1 + ( σ 2 ) 2 n 2 ] .
Generally µ 1 µ 2 = 0.

Test Statistic ( z -score):
z = ( x ¯ 1 x ¯ 2 ) ( μ 1 μ 2 ) ( σ 1 ) 2 n 1 + ( σ 2 ) 2 n 2
Generally µ 1 - µ 2 = 0.

where:
σ 1 and σ 2 are the known population standard deviations. n 1 and n 2 are the sample sizes. x ¯ 1 and x ¯ 2 are the sample means. μ 1 and μ 2 are the population means.

Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. [link] shows the result. Scouters believe that Rodriguez pitches a speedier fastball.

Pitcher Sample Mean Speed of Pitches (mph) Population Standard Deviation
Wesley 86 3
Rodriguez 91 7

What is the random variable?

The difference in mean speeds of the fastball pitches of the two pitchers

Got questions? Get instant answers now!

State the null and alternative hypotheses.

Got questions? Get instant answers now!

What is the test statistic?

–2.46

Got questions? Get instant answers now!

At the 1% significance level, what is your conclusion?

At the 1% significance level, we can reject the null hypothesis. There is sufficient data to conclude that the mean speed of Rodriguez’s fastball is faster than Wesley’s.

Got questions? Get instant answers now!

Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller.

Plant Group Sample Mean Height of Plants (inches) Population Standard Deviation
Food 16 2.5
No food 14 1.5

Is the population standard deviation known or unknown?

Got questions? Get instant answers now!

State the null and alternative hypotheses.

Subscripts: 1 = Food, 2 = No Food
H 0 : μ 1 μ 2
H a : μ 1 > μ 2

Got questions? Get instant answers now!

Draw the graph of the p -value.

This is a normal distribution curve with mean equal to zero. The values 0 and 0.1 are labeled on the horiztonal axis. A vertical line extends from 0.1 to the curve. The region under the curve to the right of the line is shaded to represent p-value = 0.0198.
Got questions? Get instant answers now!

At the 1% significance level, what is your conclusion?

Got questions? Get instant answers now!


Use the following information to answer the next five exercises. Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point.

Sample Mean Melting Temperatures (°F) Population Standard Deviation
Alloy Gamma 800 95
Alloy Zeta 900 105

State the null and alternative hypotheses.

Subscripts: 1 = Gamma, 2 = Zeta
H 0 : μ 1 = μ 2
H a : μ 1 μ 2

Got questions? Get instant answers now!

Is this a right-, left-, or two-tailed test?

Got questions? Get instant answers now!

What is the p -value?

0.0062

Got questions? Get instant answers now!

Draw the graph of the p -value.

Got questions? Get instant answers now!

At the 1% significance level, what is your conclusion?

There is sufficient evidence to reject the null hypothesis. The data support that the melting point for Alloy Zeta is different from the melting point of Alloy Gamma.

Got questions? Get instant answers now!

Questions & Answers

how do you get the 2/50
Abba Reply
number of sport play by 50 student construct discrete data
Aminu Reply
width of the frangebany leaves on how to write a introduction
Theresa Reply
Solve the mean of variance
Veronica Reply
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ... Step 2: Find each score's deviation from the mean. ... Step 3: Square each deviation from the mean. ... Step 4: Find the sum of squares. ... Step 5: Divide the sum of squares by n – 1 or N.
kenneth
what is error
Yakuba Reply
Is mistake done to something
Vutshila
Hy
anas
hy
What is the life teble
anas
hy
Jibrin
statistics is the analyzing of data
Tajudeen Reply
what is statics?
Zelalem Reply
how do you calculate mean
Gloria Reply
diveving the sum if all values
Shaynaynay
let A1,A2 and A3 events be independent,show that (A1)^c, (A2)^c and (A3)^c are independent?
Fisaye Reply
what is statistics
Akhisani Reply
data collected all over the world
Shaynaynay
construct a less than and more than table
Imad Reply
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Aschalew Reply
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400 a. what is the probability of getting more than 12,000 hits? b. what is the probability of getting fewer than 9,000 hits?
Akshay Reply
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits
Akshay
1
Bright
Sorry i want to learn more about this question
Bright
Someone help
Bright
a= 0.20233 b=0.3384
Sufiyan
a
Shaynaynay
How do I interpret level of significance?
Mohd Reply
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
Shivam
how skewness and kurtosis are used in statistics
Owen Reply
yes what is it
Taneeya

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask