Reference no: EM132912715

STAT1001 Statistical Analysis - Southern Cross University

Question 1
Use the sample house prices (in $1,000s) shown in the table below to answer the following questions:

(a) What are the mean and median for this dataset?

(b) What are the variance and standard deviation?

(c) Provide a five-number summary for house prices.

(d) Why is the median house price preferred to mean house price?

Question 2
Uber fares in a metropolitan city are known to follow a normal distribution with an average fare of $25.00 and a standard deviation of $3.00.

(a) What is the probability that a randomly selected uber fare exceeds $30.00?

(b) If an uber driver on a morning shift had 20 customers, what is the probability that the average fare per trip during the shift was less than $24.50?

(c) If an uber driver had 25 customers during a shift, what is the probability that the total fare during the shift exceeds $650?

Question 3
(a) A shop in downtown Perth is considering moving from its present location to Freemantle. One factor in this decision is the amount of time the shop's employees spend travelling to work. A random sample of 18 employees reveals that the mean and standard deviation of the time required to get to work are 37.5 and 11.3 minutes, respectively. Estimate the 95% confidence interval of the mean time to get to work. State all your assumptions and interpret your result.

(b) One factor in choosing a location for a new clothing store is the mean clothing expenditure per household in the surrounding area. A survey of 16 households reveals that the mean and standard deviation of annual expenditure on clothes is $420 and $90, respectively. Can we conclude at the 5% level that the population mean annual expenditure is less than $500? State any assumptions necessary, conduct this test and interpret your result.

Question 4
For the past few years, the number of customers of a drive-in bottleshop has averaged 20 per hour. This year, another bottleshop one kilometre away opened a drive-in window. The manager of the first shop believes that this will result in a decrease in customers. A random sample of 50 hours showed an average of 18.7 customers per hour with a standard deviation of 3.0. Can we conclude at the 5% level of significance that the manager's belief is correct?

Question 5
In recent years, fishermen have suffered financial hardship because of shortened fishing seasons, reduced catches and lower market prices. Moreover, fishermen have complained about price fluctuations and have called for a system of minimum prices. One suggestion was that the size of the catch had an immediate impact on prices and that this relationship should be clarified before potential solutions were discussed.

In an investigation of this issue, a random 12-week-period was selected to study the price of fish ($ per kg.) versus average daily catch (in 100 kgs). The data collected were analysed, and the following results were obtained:

(a) What is the estimated regression line?

(b) Interpret the estimated catch coefficient.

(c) Interpret the R2 value and comment on its strength.

(d) Does catch significantly influence the price of fish?

(e) Find the predicted level of the price if the daily catch is 75,000 kg.

Attachment:- Statistical Analysis.rar