Question

1. The owner of a restaurant that serves continental food wants to study characteristics of his customers. He decides to focus on two variables: the amount of money spent by customers and whether customers order dessert. The results from a sample of 60 customers are as follows:

• Amount spent ( =$38.54, S= $7.26)

• 18 customers purchased dessert.

1. Construct a 95% confidence interval estimate of the population mean amount spent per customer in the restaurant.      _____________
2. Construct a 90% confidence interval estimate of the population proportion of customers who purchase dessert.             ____________

2.             A computer information systems professor is interested in studying the amount of time it takes students enrolled in the Introduction to Computers course to write and run a program in Visual Basic. The professor hires you to analyze the following results (in minutes) from a random sample of nine students: 10, 13, 9, 15, 12, 13, 11, 13, 12. At the 5% level of significance, is there any evidence that the population mean is greater than 10 minutes. Do the test of hypothesis in detail?

H₀ ________H₁ ________      Graph _________________________, Critical Value(s) ___________Computed Value(s) __________

Decision _____________________________

3) Long-distance telephone calls are normally distributed with mean equal to 10 minutes and standard deviation equal to 2 minutes. If random samples of 25 calls were selected

a)             What proportion of the sample means would be between 9.80 and 10.2 minutes                 __________

b)             What proportion of the sample means would be below 9.5 and above 10 minutes               __________                                            _

c)             What should the size of n be if sampling error is within + 6 and α=.10                                ___________

4)          (mean)                                                                                                                     $ 46                                       $29                                      

         S     (Standard Deviation)                                                                                               $ 9                                           $ 8

         X_i (number of students who are making >$30,000 annually)                                     10                                            9

         n     (Sample Size)                                                                                                         37                                           26

a) Is there any evidence of a difference in the average between the two groups?

H₀ ________H₁ ________      Graph _________________________, Critical Value(s) ___________Computed Value(s) __________

Decision

b) Is there any evidence of a difference in the proportion between the two groups?

H₀ ________H₁ ________      Graph _________________________, Critical Value(s) ___________Computed Value(s) __________

Decision

c) Set up a 90% C.I.E. for the difference of two averages of two departments

Formula__________________________________,       Critical Values_________________          C.I.E. _________   _________

d) Set up a 90% C.I.E. for the difference of two population proportions

Formula__________________________________,       Critical Values_________________          C.I.E. _________   _________

5) The breaking strength of plastic bags used for packaging produce is normally distributed, with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch. What proportion of the bags have a breaking strength of

a. less than 3.17 pounds per square inch?                                                                                                                              __________

b. at least 3.6 pounds per square inch?                                                                                                                                   __________

c. between 5 and 5.5 pounds per square inch?                                                                                                                        __________

d. 95% of the breaking strengths will be contained between what two values symmetrically distributed around the mean? _____ _____           

6) Based on past data, the sample mean of the credit card purchases at a large department store is $35. Assuming sample size is 25 and the population standard deviation is 10.

a)             What % of samples are likely to have between 20 and 30?                                                                                   _________

b)             Between what two values 90% of sample means fall?                                                                                           _________

c)             Below what value 99% of sample means fall?                                                                                                       _________

d)             Above what value only 1% of sample means fall??                                                                                               _________

e)             Within what symmetrical limits of the population percentage will 95% of the sample percentages fall?            ________ _______

Answer 1

( 3c )