Question 1. A researcher seeking funds for climate change research surveys 371 randomly selected Australians and asks them: "Is global warming a major issue for Australians?" 38 replied that they believed global warming is a major issue. Construct a 95% confidence interval to estimate the proportion of all Australians who feel that global warming is a major issue.

Give the left hand side (the lower limit) of the confidence interval only

Question 2. A company's Human Resources department administers a test of "Executive Aptitude". Test scores are known to be normally distributed with a mean of 100 and a standard deviation of 15.

What score do you need to be in the top 12% of the applicant pool?

What is the score at the 55th percentile?

PayPal is interested in estimating the average number of transactions per year for their active account users.

The number of transactions per year is normally distributed. A random sample of size 25 is obtained from this population. The mean and standard deviation of the number of transactions for this sample are 81 and 9, respectively.

Calculate a 95% confidence interval for the population mean number of transactions. Give the upper limit (the right hand side of the interval) in the space provided.

Question 3. Suppose we now have a sample of size n = 500 from a normal population with

σ (sigma) = 1 and want to calculate a confidence interval for these data.

What is the numerical value of the standard error that we would use?

Question 4. An important step in creating confidence intervals for proportions is to check whether the success/failure conditions have been met otherwise the interval created will not be valid (i.e. we should not have created that interval)!

The following examples are estimating the proportion of the population who likes Brussels sprouts. Try to determine whether or not the assumptions have been met.

In a sample of 150 people surveyed, 36 liked Brussels sprouts.
Answer 1Choose...Conditions not metConditions met
In a sample of 31 people surveyed, 28 liked Brussels sprouts.
Answer 2Choose...Conditions not metConditions met
In a sample of 65 people surveyed, 25 liked Brussels sprouts.
Answer 3Choose...Conditions not metConditions met
In a sample of 104 people surveyed, 100 liked Brussels sprouts.

Question 5. Use Excel to find the Standard Normal Probability for the following questions. Don't forget to sketch the normal distribution and shade the required area.

a) What is the area in the right hand tail of the standard normal curve beyond z = 1.03?

b) What is the area under the standard normal curve between z = -1.20 and z = 0.00?

c) What is the z-value that gives the left hand tail area equal to 0.1010?

d) What is the absolute value of z such that the total area under the standard normal curve between -z and +z will be 0.9610?

Question 6. Suppose we have a sample from a population that has a uniform distribution.

As n (the size of the sample) increases, you would expect the shape of the distribution of sample means to become:

Select one:
a. more normal and more spread out
b. more uniform and more spread out
c. more uniform and less spread out
d. more normal and less spread out

Question 7. Consider a large clothing shop in Sydney. Suppose it is known that the number of business suits sold per day is normally distributed with a mean, μ = 23 and standard deviation, σ = 10. Mr Wood is employed to sell business suits. The number of business suits he sells each day for 40 days is recorded and the mean number per day calculated.

What is the probability that Mr Wood's average daily sales will be more than 29 business suits?

Question 8. Look back at your notes on sampling distributions for means. Consider selecting samples of size 30 from a skewed distribution and assume that 30 is large enough for the Central Limit Theorem to apply.

Indicate which of the following is correct:

Select one:
a. Neither the samples nor the sample means will be normally distributed
b. The sample means could be normally distributed
c. The samples will be normally distributed
d. The samples and their means will be normally distributed

Question 9. The daily exchange rates for the two-year period 2011 to 2013 between the Japanese Yen (JPY) and the Australian Dollar (AUD) can be modelled by a Normal distribution with mean, μ =81 Yen and a standard deviation , σ = 22 Yen.

Draw diagrams and use Excel to help you solve the following problems.

What is the probability that on a randomly selected day during this period, the dollar was worth less than 85 Yen?

What proportion of the days during this period will the dollar be worth between 68 and 85 Yen?

If you select a window of 225 days during this period, how many days would you expect the dollar to worth between 68 and 85 Yen? (round to nearest integer)