1. For the Gender and Ethnicity variable

a.Use Excel to generate the PivotTable showing the number of individuals in each combination of Gender and Ethnicity.Copy this into your assignment.

b.Consider a randomly selected individual from your sample.What is the probability you select a female?What is the probability you select a Maori male?If you select a female, what is the probability she is European?Maori?Pacific or Other?If you select a European, what is the probability that person is a male?Make sure you label each of these probabilities with suitable notation, i.e. using , | , etc.

c.Based on your sample, would you say that Gender and Ethnicity are likely to be independent?Why or why not?

2. Using the Income per week data:

a.What is the probability a randomly selected individual from your sample has an income over $349.99 per week?[Hint: consider using the Sort feature.]

b.Consider a randomly selected sample of 8 individuals from your sample (assume for the moment that an individual could be selected more than once into this sample).What is the distribution of the number (out of 8) that have an income greater than $349.99 per week (i.e. distribution name and parameters)?

c.Use the BINOM.DIST function in Excel to calculate the probability distribution of the number of individuals in the sample of 8 in b who have an income over $349.99 per week.Copy this table into your assignment.What is the most likely number (i.e. the mode)?What is the probability none in the sample have an income over $349.99 per week?What is the probability that more than half do?What is the expected number of individuals?Finally, what is the standard deviation of the number?Make sure you label each of these quantities with suitable notation, i.e. using P, E, etc.

d.If an individual could not be selected more than once into the sample, what implications does this have for the binomial assumptions?

3. Using the Hours worked per week data:

a.Calculate the mean and (sample) standard deviation of these data.

b.Now, assume you select an individual from a normally distributed population with mean and standard deviation corresponding to your values in a above (i.e. use them as and.What is the probability that this person works more than 40 hours per week?What is the probability they work less than 20 hours per week?What is the probability they work between 35 and 45 hours per week?For each of these probabilities, give also the Excel command you've used to obtain them.

c.Again, assuming the population of Hours worked is normally distributed, what is the 90th percentile of this distribution?Give the Excel command you use to obtain this percentile.

d.Comment on the likely validity of the normal distribution in this case.

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Never Never Other Never Never Previously Married Other Never Married Married Other Never Previously Previously Married Qualification PostSchool Vocational Yes Vocational Yes Degree Yes School No Degree Yes School No School No Degree Yes School No Vocational Yes None No Vocational Yes School No Degree Yes None No Degree Yes School No School No Vocational Yes Vocational Yes None No School No Vocational Yes Vocational Yes School No None No None No School No School No Vocational Yes None No Degree Yes School No Vocational Yes School No None No School No School No Degree Yes Vocational Yes School No School No School No Degree Yes Hours 70 32 60 35 40 45 40 45 4 40 40 8 50 45 40 38 20 40 32 44 35 32 45 42 50 40 27 17 45 8 40 13 9 40 21 38 5 40 50 38 40 10 50 40 Male Male Male Female Female Female Female Male Female Male Female Female Male Female Male Male Female Male Male Male Female Female Female Female Female Female Male Male Male Male Female Male Male Male Female Male Male Female Female 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