All work must be shown to qualify for partial credit. Also check to make sure all your work is legible and clear before submitting it. Answer 4 out of 5 questions. You should use Excel to answer most of the questions.
1. Consumer Reports posts reviews and ratings of a variety of products on its website. The following is a sample of 20 speaker systems and their ratings. The ratings are on a scale of 1 to 5, with 5 being best.
Speaker Rating Speaker Rating
Infinity Kappa. 6.1 4.00 ACI Sapphire III 4.67
Allison One 4.12 Bose 501 Series 2.14
Cambridge Ensemble II 3.82 DCM KY-212 4.09
Dynaudio Contour 1.3 4.00 Eosone RSF 1000 4.17
Hsu Rsch. HRSW 12V 4.56 Joseph Audio RM7 si 4.88
Legacy Audio Focus 4.32 Martin Logan Aerius 4.26
Mission 73Ii 4.33 Omni Audio SA 12.3 2.32
PSB 400i 4.50 Polk Audio RT 12 4.50
Snell Acoustics D IV 4.64 Sunfire True Subwoofer 4.17
Thiel CS 1.5 4.20 Yamaha NS- A636 2.17
Compute the mean and the median.
Compute the first and third quartiles.
Compute the standard deviation.
What are the z-scores associated with Allison One and Omni Audio?
Do the data contain any outliers? Explain.
2. A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents have boycotted goods for ethical reasons.
In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?
In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?
In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons?
In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? Also find the standard deviation.
3. The Webster National Bank is reviewing its service charges and interest-paying policies on checking accounts. The average daily balance on personal checking accounts is $550, with a standard deviation of $150. In addition, the average daily balances are normally distributed.
a) What percentage of personal checking account customers carry average daily balances in excess of $800?
b) What percentage carry average daily balances below $200?
c) What percentage carry average daily balances between $300 and $700?
d) The bank is considering paying interest to customers carrying average daily balances in excess of a certain amount. If the bank does not want to pay interest to more than 5% of the customers, what is the minimum average daily balance it should be willing to pay interest on?
4. The following 20 observations are for two quantitative variables, x and y (Data file is Scatter and presented on Classes).
a) Create a scatter chart for these 20 observations,
b) Fit a linear trend line to the 20 observations. What can you say about the relationship between the two quantitative variables?
c) Find the correlation coefficient and the covariance. Discuss their relevance to the relationship between x and y.
5. A Daytona Beach nightclub has the following data on the age and marital status of 140 customers.
Develop a joint probability table using the data.
Use the marginal probabilities to comment on the age of customers attending the club.
Use the marginal probabilities to comment on the marital status of customers attending the club.
What is the probability of finding a customer who is single and under the age of 30?
If a customer is under 30, what is the probability that he or she is single?
Is marital status independent of age? Explain, using probabilities.