Variables Problem 1 Give two examples of variables measured on a ratio scale z S
ID: 3315370 • Letter: V
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Variables Problem 1 Give two examples of variables measured on a ratio scale z Scores and p values for scores and sample means Problem 2 A population of scores is distributed like a normal distribution with mean =40 and standard deviation oH12 a) What is the probability to find scores X in this population that have values smaller than 342 b) Let us assume we take samples from this population that are composed of n-9 scores. What is the probability to find sample means M smaller than 34? t Tests for single samples Problem 3 A researcher wants to show that the IQ scores are increasing from generation to generation. The researcher uses an IQ test from 1980. In 1980, IQ scores determined via this test were distributed for high school students like a nomal distribution with a population mean of 100·The population variance is unknown. In 2015, the researcher tests n= 16 students and obtains an IQ mean value of M=121 with a variability expressed in Sum of Squares of 6000. Conduct a one-tailed t test at a significance level of 1% in order to find out whether the difference between the observed sample mean IQ and the population mean IQ from 1980 is statistically significant.Explanation / Answer
Q2.
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 40
standard Deviation ( sd )= 12
a.
P(X < 34) = (34-40)/12
= -6/12= -0.5
= P ( Z <-0.5) From Standard Normal Table
= 0.3085
b.
mean of the sampling distribution ( x ) = 40
standard Deviation ( sd )= 12/ Sqrt ( 9 ) =4
sample size (n) = 9
P(X < 34) = (34-40)/12/ Sqrt ( 9 )
= -6/4= -1.5
= P ( Z <-1.5) From Standard NOrmal Table
= 0.06681
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