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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

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State the null and alternative hypotheses.

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What is the test statistic?

–2.46

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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.

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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?

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State the null and alternative hypotheses.

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

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

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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

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

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What is the p -value?

0.0062

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Draw the graph of the p -value.

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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.

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Questions & Answers

the probability of an event occuring is defined as?
James Reply
The probability of an even occurring is expected event÷ event being cancelled or event occurring / event not occurring
Gokuna
what is simple bar chat
Toyin Reply
Simple Bar Chart is a Diagram which shows the data values in form of horizontal bars. It shows categories along y-axis and values along x-axis. The x-axis displays above the bars and y-axis displays on left of the bars with the bars extending to the right side according to their values.
Muhammad
statistics is percentage only
Moha Reply
the first word is chance for that we use percentages
muhammad
it is not at all that statistics is a percentage only
Shambhavi
I need more examples
Luwam Reply
how to calculate sample needed
Jim Reply
mole of sample/mole ratio or Va Vb
Gokuna
how to I solve for arithmetic mean
Joe Reply
Yeah. for you to say.
James
yes
niharu
how do I solve for arithmetic mean
Joe Reply
please answer these questions
niharu
add all the data and divide by the number of data sets. For example, if test scores were 70, 60, 70, 80 the total is 280 and the total data sets referred to as N is 4. Therfore the mean or arthritmatic average is 70. I hope this helps.
Jim
*Tan A - Tan B = sin(A-B)/CosA CosB ... *2sinQ/Cos 3Q = tan 3Q - tan Q
Ibraheem Reply
standard error of sample
Umar Reply
what is subjective probability
Avela Reply
how to calculate the Steadman rank correlation
David
what is sampling? i want to know about the definition of sampling.
anup Reply
what is sample...?
Abdul Reply
In terms of Statistics or Research , It is a subset of population for measurement.
Da
can you solve this problem
Gayanne Reply
yes
Harry
which problem
Larwubah
what is the meaning of correlation ratio?
Nayeem
in 2018,walewale hospital recorded 2500cases of infection it was seen that out of this number 350 cases are rti 150 were bronchitis 300 cases were otitis media the rest were peptic ulcer cases calculate proportion of peptic ulcer and percentage of bronchitis
Ayana Reply
what is statistics
peter
yo
Kailesh
12% bronchitis cases
Rajat
what is the frequency
okoh Reply
Frequency is the number of all object which is comes from population or sample size
Faiqa
Denoted by f
Faiqa
number of all objects?
Amir
frequency is the rate of occurrence of an object
Leek
Explain nominal and ordinal variables
Oyinlola
 nominal variables are those variable which is used to “name,” a series of values.
Amir
while  ordinal scales provide good information about the order of choices,for example in a customer satisfaction survey.
Amir
what is the difference between Mean and Varience?
Amir
Sum of total object, divided by number of object is called mean
Faiqa
variance?
Amir
faiqa U didn't clear me.Sorry
Amir
what is df in statistics
Oyinlola
degre of freedom
Amir

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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