Q.1 Refer to Dataset 1 on Canvas/Teams.The annual incomes for a sample of 200 firstyear accountants were recorded. Draw a histogram and describe its shape,including discussion on whether its skewed...

Q.1

Refer to Dataset 1 on Canvas/Teams.

The annual incomes for a sample of 200 first
year accountants were recorded. Draw a histogram and describe its shape,
including discussion on whether its skewed (positive or negative), or is
symmetrical, and also on the variability around the mean.

Q.2

Refer to Dataset 2 on Canvas/Teams.

An analyst employed at a commodities trading
firm wanted to explore the relationship between prices of grains and livestock.
Theoretically, the prices should move in the same direction because, as the
price of livestock increases, more livestock are bred, resulting in a greater
demand for grains to feed them. The analyst recorded the monthly grains and
livestock subindexes for 1971 to XXXXXXXXXXSubindexes are based on the prices of
several similar commodities. For example, the livestock subindex represents the
prices of cattle and pigs.) Draw a scatter diagram of the two subindexes. In
general, do the two subindexes move in the same direction?

Q.3

Refer to Dataset 3
on Canvas/Teams.

Find the mean and standard deviation of the
household debt (DEBT) of the respondents in the 2013 survey. If we assume that
debt is not bell-shaped describe what the mean and standard deviation tell you.

Q. 4

Refer to Dataset 4 on Canvas/Teams.

A professional income tax preparer recorded the amount of tax rebate and
the total taxable amount of a sample of 80 customers. Compute whichever
statistics you need to determine whether tax rebates increase as the taxable
income increases.

Q.5

This question does not require any dataset to
be downloaded.

Statisticians determined that the mortgages of
homeowners in a city is normally distributed with a mean of €250,000 and a
standard deviation of €50,000. A random sample of 100 homeowners was drawn. What
is the probability that the mean is greater than €262,000?

Q.6

Refer to Dataset 5 on Canvas/Teams.

A survey of 80 randomly selected companies asked
them to report the annual income of their presidents. Assuming that incomes are
normally distributed with a standard deviation of €30,000, determine the 90%
confidence interval estimate of the mean annual income of all company
presidents. Interpret the statistical results.

Q. 7

Refer to Dataset 6 on Canvas/Teams.

In the midst of labour–management negotiations,
the president of a company argues that the company’s blue-collar workers, who
are paid an average of €30,000 per year, are well paid because the mean annual
income of all blue-collar workers in the country is less than €30,000. That
figure is disputed by the union, which does not believe that the mean
blue-collar income is less than €30,000. To test the company president’s
belief, an arbitrator draws a random sample of 350 blue-collar workers from
across the country and asks each to report his or her annual income. If the
arbitrator assumes that the blue-collar incomes are normally distributed with a
standard deviation of €8,000, can it be inferred at the 5% significance level
that the company president is correct?

Q. 8

Refer to Dataset 7 on Canvas/Teams.

A national survey conducted by NZ Research
Institute asked a random sample of 974 NZ adults how they felt about doing
their taxes. Those who hate or dislike doing their taxes were asked the reason.
The responses are: 1 = Pay too much tax, 2 = Complicated/too much paperwork, 3
= Inconvenient/time consuming, 4 = Don’t like how government uses tax money, 5
= Owe the government money. 6 = Other. Estimate with 95% confidence the proportion
of NZ adults who had indicated that they hated or disliked doing their taxes
who hated or disliked it because they don’t like how the government uses tax
money.

Questions 9 and 10 do not require any dataset
to be downloaded.

Q.9

A
consumer group wants to estimate the mean water bill for the month of July for
single family homes in Auckland. Based
on studies conducted in other large cities, the standard deviation is assumed
to be $30. The group needs to estimate the mean bill for July within ±$6 with 95%
confidence. Given this information,

i)
how many single family homes
should this consumer group select for this estimation?

ii)
If you wish to reduce the
margin of error to $5, would you still select the sample size as in i) above ?
Justify your answer without any calculations.

Q. 10

For the past few years, the number of customers of
a Costa mobile order-ahead store in Oxford has averaged 20 per hour, with a
standard deviation of 3 per hour. This year, another coffee mobile order-ahead
store 1 mile away opened a drive-up window. The manager of the Costa mobile
order-ahead store believes that this will result in a decrease in the number of
customers. The number of customers who arrived during 36 randomly selected
hours was recorded. Can we conclude at the 5% significance level that the
manager is correct?