1. Records at ABC Inc. show information on whether customers are former or new and whether they are credit customers or cash customers. See below.
|
|
Former
|
New
|
Total
|
|
Credit
|
336
|
80
|
416
|
|
Cash
|
144
|
240
|
384
|
|
Total
|
480
|
320
|
800
|
If you choose a customer at random, then find the probability that the customer
a. was new and paid in cash.
b. was a former customer.
c. used credit, given that the customer was new.
2. Of federal taxpayers who itemize their deductions and have adjusted gross incomes between $35,000 and $50,000, the dollar amount of gifts to charity claimed on Schedule A is normally distributed with a mean of $549 and a standard deviation of $168.
a. What percentage of taxpayers with adjusted gross incomes between $35,000 and $50,000 will claim less than $400 in gifts to charity on Schedule A?
b. What percentage of taxpayers with adjusted gross incomes between $35,000 and $50,000 will claim between $500 and $600 in gifts to charity on Schedule A?
c. The IRS decides to audit any return for which the deduction for gifts exceeds that for 99% of those who itemize and have adjusted gross incomes of between $35,000 and $50,000. Above what dollar figure is a tax return automatically flagged according to this criterion?
3. A food company is planning to market a new kind of cereal; however, before marketing this product, the company wants to find the percentage of people who will like it. The company's research department selected a random sample of 500 persons and asked them to taste the cereal. Of these 500 people, 290 said they liked it.
a. Compute the 95% confidence interval for the percentage of the population that will like the cereal.
b. Interpret this confidence interval.
c. How many people should be selected in order to be 99% confident of being within 1% of the population percentage of people who will like the cereal?
4. Carleton Chemical claims that they can produce more than 800 tons of meladone on average per week. A random sample of 36 weeks of production yields the following results.
Sample Size = 36
Sample Mean = 823
Sample Standard Deviation = 79.8
Does the sample data provide sufficient evidence to support the claim made by Carleton Chemical (using a = .10)? Use the hypothesis testing procedure outlined below.
a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide sufficient evidence to support the claim made by Carleton Chemical (using a = .10)?