Levene’s test for testing variances

Instruction: This is a 3 hours exam. You are giving an extra 30min to submit your exam. The clock start when you open the exam. Use this word document to provide your answers and copy and paste any supporting output or graph generated in SPSS. Once you are done submit back in canvas, as you usually do for the homework. No late submission will be accepted and the system will shut down after your time elapses.

Consider the female health data set “FHEALTH” available on Canvas. Based on this data set answer all questions below
1- Consider the variable “Age”, based on this variable answer the following questions
a- Report the mean, standard deviation, IQR, and skewness for the age variable.

b- What is the shape of the variable age?

c- Do you think that the variable age came from a normal distribution? Why?

2- Consider the variable “Height”, based on this variable answer the following questions.
a- Construct a 99% confidence interval for the variable “Height”.

b- Test if the mean Height is significantly different from 64 inches

i- The test statistic is ……………………………………………………………

ii- The degrees of freedom are …………………………………………………..

iii- The P value and conclusion ……………………………………………………

3- Suppose that a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. The study is to be conducted in a large suburb of a major city. A sample of 14 recent fires in this suburb is selected. The amount of damage, y, and the distance between the fire and the nearest station, x, are given below. We are interested in building a regression model to predict fire damage y, given the distance from the fire x.

Distance 3.4 1.8 4.6 2.3 3.1 5.5 0.7 3.0 2.6 4.3 2.1 1.1 6.1 4.8
Damage 26.2 17.8 31.3 23.1 27.5 36.0 14.1 22.3 19.6 31.3 24.0 17.3 43.2 36.4

a- Find the Pearson and Spearman correlations between the distance from the fire station and the amount of damage.

b- Is the predictor distance significant? What is the test statistic and p value?

c- What is the amount of variation explained in the model?

d- What is the standard error of the estimated regression line?

e- Use the final regression equation to predict the damage caused by the fire that is 6.5 miles away from the nearest station.

4- In recent years, concerns have been expressed about adverse health effects from amalgam dental restorations, which include mercury. The table below shows results from a study in which some patients were treated with amalgam restorations and others were treated with composite restorations that don’t contain mercury. Use a 5% level of significance to test for independence between the type of restoration and sensory disorders. Do amalgam restorations appear to affect sensory disorders?

``Amalgam Composite``

Sensory Disorder 10 7
No Sensory Disorder 9 15

a- What is the value of your test statistics?

b- What are the degrees of freedom for this test?

c- What is the p value for this test?

5- Listed below are the amounts of carbon monoxide (mg/cigarette) in samples of king size, 100 mm menthol, and 100 mm non menthol cigarettes. Use 5% significance level to test the claim that the three categories of cigarettes yield the same amount of carbon monoxide (hint: One way ANOVA).

King Size 16,16,16,16,16,17,16,15,16,14,16,16,16,16,16,14,16,16,14,18,15,16,14,16,16
Menthol 15,17,19,9,17,17,15,17,15,17,17,15,17,17,18,11,18,3,17,14,15,22,16,7,9
Non Menthol 4,19,17,18,18,13,17,15,15,12,18,17,18,16,3,18,15,18,15,17,15,15,7,16,14

a- What is the test statistic and p value to test the hypothesis that all means are the same?

b- What is the test statistic and p value for Levene’s test for testing variances homogeneity for the groups?

c- Perform a multiple testing process and state which groups are significantly different in their mean carbon monoxide.