Problem 1

A hair salon reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution.

1. Construct the 90% confidence interval for the average number of customers who visit the salon on weekdays.
2. Construct the 99% confidence interval for the average number of customers who visit the salon on weekdays.
3. What happens to the width of the interval as the confidence level increases?

Problem 2

The information gathered from opinion polls and political surveys is becoming so increasingly important for candidates on the campaign trail that it is hard to imagine an election that lacks extensive polling. An NBC survey of 1000 adults asked people's preferences on candidates and issues prior to the midterm 2010 elections.

Question 1: In general, do you approve or disapprove of Obama handling the Gulf Coast oil spill in 2010 and Bush's handling of Katrina in 2006?

	Obama 2010	Bush 2006
Approve	50%	36%
Disapprove	38%	53%
Not sure	12%	11%

Question 2: Which are more important to you in your vote for Congress this November: domestic issues (economy, healthcare, immigration) or international issues (Afghanistan, Iran, terrorism)?

	Obama 2010	Bush 2006
Domestic issues	73%	43%
International issues	12%	28%
Both equally important	15%	28%

Construct 95% confidence intervals to:

1. Compare approval rates for handling the Gulf Coast oil spill and the Hurricane Katrina
2. Compare importance of domestic issues in 2006 and 2010.

Problem 3(Chi Distribution)

A rent-to-own (RTO) agreement appeals to low-income and financially distressed consumers. It allows immediate access to merchandise, and by making all payments, the consumer acquires the merchandise. At the same time, goods can be returned at any point without penalty. A rent study documents that 65% of RTO contracts are returned, 30% are purchased, and the remaining 5% default. In order to test the validity of this study's findings, a researcher looks at the transaction data of 420 RTO contract, of which 283 are returned, 109 are purchased, and the rest defaulted.

1. Set up the competing hypothesis to test whether the returns, purchase, and default probabilities of RTO contracts differ from 0.65, 0.3, and 0.05, respectively.
2. Compute the value of the test statistic.
3. Conduct the test at the 5% level of significance and interpret the test results.

Problem 1

In 2010, Apple introduced the iPad, a tablet-style computer that its former CEO Steve Jobs called a "truly magical and revolutionary product." Suppose you are put in charge of determining the age profile of people who purchased iPad in the US. Explain in detail the following sampling strategies you could use to select a representative sample.

1. Simple random sampling.
2. Stratified random sampling.
3. Cluster sampling.

Problem 2

Random samples of size n = 400 are taken from a population with p = 0.10.

1. Construct the centerline and the upper and lower control limits for the p-bar chart.
2. Suppose six samples of size 400 produced the following sample proportions: 0.06, 0.11, 0.09, 0.08, 0.14, and 0.16. Plot these values on the p-bar chart.
3. Is the production process under control? Explain.

Problem 3

A seminal study conducted by scientists at the University of Illinois found evidence of improved memory and reasoning for those who took three vigorous 40-minute walks a week over six months. As a public health manager in Miami, Florida, you would like to estimate the proportion of adults who follow such a walking regimen.

• Discuss the sampling bias in the following strategies where people are asked if they walk regularly:

1. Randomly selected adult beachgoers in Miami.
2. Randomly selected Miami residents who are requested to disclose the information in prepaid envelopes.
3. Randomly selected Miami residents who are requested to disclose the information on the organization's website.
4. Randomly selected adult patients at all hospitals in Miami.

• Explain how you can obtain a representative sample based on the following sampling strategies:

1. Simple random sampling.
2. Stratified random sampling.
3. Cluster sampling.