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SDA 101 Students Chi-Square Test of Independence c2
SPSS output for Regression Tests of Significance Normal distribution
SPSS Instructions Exam questions More Questions
Here are the answers to the following questions
Question Nine
Here is my answer to this question use the links to view SPSS output.
Assumptions and Definitions
The variable of interest is the workload measured as relative I/O content.
To test whether the population is normally distributed we look at the Shapiro-Wilk sig. if this is greater than 0.05 then the data is normally distributed.
Look at table Test of Normality
Hypotheses
Null Hypothesis: m = 1
Alternative Hypothesis m ¹ 1
Testing the Null hypothesis that the true population workload measure is 1 against the alternative hypothesis that the population workload measure is now different to 1.
Test Data
Read directly from Descriptives table
Test statistic
Read from the table marked One-Sample Test
t 23 = 2.063 23 are the Degrees of Freedom (df)
P-value
We read P-value directly as SPSS always does two sided tests
Decision
So looking at our example we can see that the p-value is more than 0.05 so we will accept the Null Hypothesis.
Conclusion
The results are not significant indicating that there is insufficient evidence to suggest that workload is different to the base rate of 1 at 5% significance level.
Question Seven from previous exam
Part a
`x = 57.16 s = 8.21
Make sure that you use the sample standard deviation rather than the population standard deviation.sn - 1 or s on the calculator
Part b i
Part b ii
The distribution looks symmetrical, the mean and the median are almost equal, 57 and 59 respectively.
Part c
You have not yet learnt the t distribution but we use t instead of z when we have s sample standard deviation rather than s population standard deviation and the sample size is less than 30.
Substituting the values in
`x = 57.16
t = 2.624
s = 8.21
Ö n Ö 15
57.16 ± 2.624 2.1198
57.16 ± 5.5624
51.5976 < m < 62.7224
So we are 98 % confident that the true mean air pollution index lies between 51.60 and 62.72.
Remember that we are 98% confident or sure, it is not a probablity of 98%. The true population mean is either in the interval created or not in the interval. We will never know whether the interval contains the population mean as if we created 100 intervals, then about 98 would contain the true mean but 2 would not and there is no means of telling them apart.
Part d
Yes because of the small sample size the only way the sampling distribution of the mean recordings of the air pollution will be normal is only if the parent population is normal. The CLT does not apply as the sample size is not large enough.
Part e
Definitions and Assumptions
Let the variable of interest be the pollution index.
We will assume that the pollution index population is normally distributed the stem and leaf diagram gives evidence for this as the sample looks normal. The CLT cannot be applied as the sample size is too small. We will assume that it is a random sample and the values are all independent
Hypotheses
Test Data
`x = 57.16 s = 8.21
Test Statistic assuming the null hypothesis is true
P-Value
Decision
Accept Ho
Conclusion
The results are not significant indicating that there is insufficient evidence to suggest that the pollution index is greater than 55. There seems to be no concern for EPA
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