STAT177 Assignment #3

Due February 20, 2008

Each question is worth 1 mark unless otherwise stated.

Question 1

Companies generally have fluctuations in their earnings from month to month. A company tried a new marketing strategy during its slow period in order to have monthly earnings be more consistent from one month to the next. Its monthly earnings had been normally distributed with a mean of $452,600 and standard deviation of $87,200. For a systematic random sample of 6 months, these were the results:

436000

357800

479500

562100

555900

598700

The hypothesis was conducted at a 5% level of significance.

a) State the null and alternative hypotheses.

b) State the value of the test statistic.

c) State the conclusion about the monthly earnings being more consistent.

d) Suppose a level of significance had not been chosen. Why would the same conclusion be reached?

Question 2

A realtor wanted to determine if there had been a significant decrease in the average home price of $415,000 from six months ago due to recessionary factors. A random sample of 20 homes had the following results (in thousands of dollars):

380.9	432	388.2	441.5	373.3
340.2	311.5	320.8	389	298.1
355.9	517.4	397	428	362.6
504.9	387.5	401.7	364	1347.7

The hypothesis was conducted at a 5% level of significance.

a) What is the appropriate test for this data. State all the reasons why this is the appropriate test. (4 marks)

b) State the value of the test statistic.

c) State the conclusion.

d) Identify the outlier.

e) Conduct the analysis without the outlier. State one reason why the conclusion changes.

Question 3

An urban planner wanted to determine if there had been a change in the percentage of people commuting more than 25 km to work due to the effects of both urban sprawl and more people living in the downtown core. Based on records from 5 years previous, the percentage at the time was 14.5%. In a survey of 400 people, 62 commute more than 25 km to work. The hypothesis was conducted at a 5% level of significance.

a) State the null and alternative hypotheses.

b) State the value of the test statistic.

c) State the conclusion.

d) Based on the 95% confidence interval, what is the maximum percentage of people commuting more than 25 km to work?