Chapter 3 Flashcards
A sample mean is a ____ estimate and we do not know how close it is to the population mean
Point
You have the following sample data; a sample size of 7, a mean if 8 and a standard deviation of 4.2. From this, what is the standard error
1.58
How do you find the standard error
SD divided by the square root of the sample number -1
With the previous data set, convert the score of 10 to a z score
0.48
What is the 95% confidence interval for the data
4.90 to 11.10
If you have a negative z score it will be below the mean: true or false
True
In another study you have a standard deviation of 12, a mean of 20 and a sample size of 50. What is the standard error
1.70
In error bar charts the larger the confidence interval the ____ the line is through the mean
Longer
In order to use the standard normal distribution you need to transform the scores in the sample to the standard normal scores. This is achieved by which of the following? What is the result called?
Subtracting the mean from each score and then dividing by the standard deviation. The result is called a z score
Inferential statistics deal with:
Making conclusions and generalisations about population/s from our sample data
Normal distribution theory tells us that for large samples, 95% of sample means lie within how Mann standard deviations above and below the population mean.
1.96
Sampling distributions tend to be what in shape?
Normal
Suppose that some assessment results for two types of offenders (sex offenders and violent offenders) were 60 and 60 respectively. Which type of offender did better in comparison to other offenders on the treatment course and which may need further treatment? The group means and SDs are 50 and 9 sex offenders and 45 and 3 for violent offenders
To make such comparisons you need to convert the assessment results into z scores. This the violent offender scored better in comparisons to other offenders on his treatment course and you may perhaps want to refer the sex offender for more treatment.
((60-50) / 9 = 1.11 (z score for sex offender)
((50-45) / 3 = 1.66 (z score for violent offender)
Violent offenders z score is slightly better so they don’t need more treatment
How do you calculate the z score
(Sample number - mean) divided by the standard dev.
Eg
Sample number = 60
Mean = 50
SD = 9
60-50 divided by 9
10 divided by 9 = 1.11
Z score = 1.11
The mean of a set of IQs is 100 and the standard dev is 15. The z score for one student is +2.20. What does this mean?
Only 1.39% of scores are equal to or greater than this students score - they are very bright
The standard error has been calculated as 2.6 and the sample mean is 10.00. Thus the 95% confidence interval lies between:
4.904 to 15.096
There is substantial overlap between two sets of confidence intervals on an error bar chart. The chart shows confidence intervals for boys and girls on a depression questionnaire. What could we make of this.
We can be 95% confident that the population means are within the intervals indicated on the charts. As there is much overlap between the two sets of confidence intervals we cannot be sure whether there is a difference in the population means. It seems likely that there is no difference but we cannot draw any firm conclusions.
To calculate confidence intervals we need make use of
Probability distributions
We do not know whether the pattern of results found in our sample accurately reflects what is happening in the population or if it is the result of _____ error
Sampling
What is the probability 1 in 12 expressed as a percentage
8.33%
1 / 12 = 0.083
0.083 x 100 = 8.33 %
Which of the following is not a conditional probability
The probability of falling down stairs
Which of the following is the correct statement
The mean of several sample means gives the best estimate of the population means
Which type of graphs can display confidence intervals
Error bar charts
You have the IQs of a set of people. The mean of IQs is 100. The standard deviation is 15. One student scored 90 on the test. This produced a z score of -0.7. What does this mean?
The table tells us that 75.80% if people in the set would have IQs equal to or greater than the student. In other words the student is not exceptionally intelligent
Given a set of data how would you calculate the 95% confidence intervals
To work out the 95% confidence interval you have to multiple the standard error by 1.96
