ࡱ > ' bjbjVV 4 < < ` ` 8 \ K L sU r r r T U U U U U U sW Z B U - r r r r r U -U r F T r T N tS bZ' F O 4 T CU 0 sU P p WZ WZ h tS tS & WZ S P r r r r r r r U U r r r sU r r r r WZ r r r r r r r r r ` i : Web Calculator Exercise 1
Descriptive Statistics
The table below presents data for a sample of people who completed a religious survey.
AgeGenderDenominationChurch Attendance56174462654926549115272955114247223671544922633112655295401756218647263562952211025024551110650176431103
In this table, the numbers in the gender, denomination, and church attendance columns represent the following.
Gender
Male
Female
Denomination
Episcopal
Lutheran
Methodist
Presbyterian
Other mainline Protestant
Baptist
Other Evangelical Protestant
Pentecostal
Charismatic
Non-denominational
Catholic
Other
Church Attendance
less than once a month
once a month
a few times a month
once a week
twice a week
three or more times a week
What is the mean age of this sample? What is the standard deviation?
Create a frequency distribution table for denomination.
What is the percentage of people who identify themselves as Baptist in this sample?
What is the mode of church attendance?
The results of a recent survey indicate that the average new car costs $23,000, with a standard deviation of $3,500. The price of cars is normally distributed.
What is a Z score for a car with a price of $ 33,000?
What is a Z score for a car with a price of $30,000?
At what percentile rank is a car that sold for $30,000?
In one elementary school, 200 students are tested on the subject of Math and English. The table below shows the mean and standard deviation for each subject.
MeanSDMath679.58English 7812.45
One students Math score was 70 and the same individuals English score was 84. On which exam did the student do better?
Suppose you administered an anxiety test to a large sample of people and obtained normally distributed scores with a mean of 45 and standard deviation of 4. Do not use web-calculator to answer the following questions. Instead, you need to use the Z distribution table in Appendix A in Jacksons book.
If Andrew scored 45 on this test. What is his Z score?
If Anna scored 30 on this test. What is her Z score?
If Bills Z score was 1.5, what is his real score on this test?
There are 200 students in a sample. How many of these students will have scores that fall under the score of 41?
The table below shows Psychology exam scores, Statistics Exam scores, and IQ scores for a random sample of students. What can you observe in the relationship between IQ and psychology, psychology and statistics, and IQ and statistics? Using a web-calculator, obtain the Pearsons r and coefficient of determination for the following relationships.
Between the IQ and psychology scores
Between the IQ and statistics scores
Between the psychology scores and statistics scores.
Student number IQ PsychologyStatistics1011424949102100303210310336381041214441105120354210611547431071013735108109454710911130431101154946
In a study on caffeine and stress, college students indicated how many cups of coffee they drink per day and their current stress level on a scale of 1 to 10. The table shows the survey results. Using a web-calculator, obtain the appropriate correlation coefficients.
Number of cups of coffeeStress level 35234369541271035
Web Calculator Exercise 2
Z test & One sample t-test
A researcher is interested in whether students who attend private high schools have higher average SAT Scores than students in the general p o p u l a t i o n . A r a n d o m s a m p l e o f 9 0 s t u d e n t s a t a p r i v a t e h i g h s c h o o l i s t e s t e d a n d a n d a m e a n S A T s c o r e o f 1 0 3 0 i s o b t a i n e d . T h e a v e r a g e s c o r e f o r p u b l i c h i g h s c h o o l s t u d e n t i s 1 0 0 0 ( = 2 0 0 ) .
I s t h i s a o n e - o r t w o t a i l e d t e s t ?
W h a t a r e H 0 a n d H a f o r t h is study?
Compute Z obt
What is the Z critical value (Z cv ) using a 0.05 alpha level?
Should H0 be rejected? What should the researcher conclude?
Determine the 95 % confidence interval for the population mean, based on the sample mean.
A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners pulses would be slower. He obtained a random sample of 10 long-distance runners. He measured their resting pulses. Their pulses were 45, 45, 64, 50, 58, 49, 47, 55, 50, 52 beats per minute. The average resting pulse of athletes in the general population is normally distributed with a pulse rate of 60 beats per minute.
What statistical test should be used to analyze the data?
Is this a one- or two- tailed test?
What are H0 and Ha for this study?
Find tcv from appendix A in Jacksons text.
Compute t obt
Should H0 be rejected? What should the researcher conclude?
A researcher hypothesizes that people who listen to music via headphones have greater hearing loss and will thus score lower on a hearing test than those in the general population. On a standard hearing test, the overall mean for the general population is 22.5. The researcher gives this same test to a random sample of 12 individuals who regularly use headphones. Their scores on the test are 15, 14, 20, 20, 25, 22, 21, 19, 16, 17, 21, 22.
What statistical test should be used to analyze the data?
Is this a one- or two- tailed test?
What are H0 and Ha for this study?
Compute t obt
Should H0 be rejected? What should the researcher conclude?
Web Calculator Exercise 3
T test for independent groups and dependent groups (Two-group designs)
An LU professor is interested in whether there is a difference between undergraduate students and graduate students in the amount of time spent praying each day. The professor gathers information from random samples of undergraduate and graduate students on the LU campus. The amount of time praying is normally distributed and is measured on an interval/ratio scale.
GraduateUndergraduate1591711109136115176
What statistical test should be used to analyze the data?
Is this a one- or two tailed test?
Identify H0 and Ha for this study.
Conduct the appropriate analysis. Should H0 be rejected?
A teacher wants to investigate whether there is a difference between male and female students in the amount of time they spend studying for statistics. The table below shows the amount of time students spend studying statistics each week. The amounts of time spent studying are normally distributed.
MaleFemale2725252919181023162017151519What statistical test should be used to analyze the data?
Is this a one- or two tailed test?
Identify H0 and Ha for this study.
Conduct the appropriate analysis. Should H0 be rejected?
A researcher is interested in whether listening to music helps or hinders test-performance. To control for differences in cognitive level, this researcher decides to use a within-participants design. He selects a random sample of participants and has them study different material of equal difficulty in both the music and no music conditions. Participants take a 20-item quiz on the material. The table below shows the scores on the quiz. The study is completely counterbalanced to control for order effects. The scores obtained are measured on an interval-ratio scale and are normally distributed.
Music No Music 171716181517161718191818
What statistical test should be used to analyze the data?
Is this a one- or two tailed test?
Identify H0 and Ha for this study.
Conduct the appropriate analysis. Should H0 be rejected? What should the researcher conclude?
Calculate the 95 confidence interval.
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