Chapter 11 Review

From experience, the owner of an ice-cream shop has found that 60% of all sales of ice-cream cone are for one-scoop cones, 30% are for two-scoop cones, and the remaining 10% are for three-scoop cones. Recently, the shop added frozen-yogurt cones to its menu. A random sample of 250 frozen yogurt-cone sales revealed the following distribution:
Number of scoops          Number of sales
one                             154
two                             84
three                           12
The owner wishes to know whether the pattern of sales for frozen-yogurt cones differs from that of ice-cream cones. Which one of the following pairs of null and alternative hypotheses are appropriate for this test?

• H0: The distribution of the variable “number of scoops” is the same for frozen yogurt cones as it is for ice cream cones.
  Ha: The distribution of the variable “number of scoops” is different for frozen yogurt cones than it is for ice cream cones.
• H0: The observed counts for “number of scoops” are the same as the expected counts.
  Ha: At least one of the observed counts for “number of scoops” is different from the corresponding expected count.
• H0: Ice-cream cone sales and frozen-yogurt cone sales are independent.
  Ha: Ice-cream cone sales and frozen-yogurt cone sales are dependent.

From experience, the owner of an ice-cream shop has found that 60% of all sales of ice-cream cone are for one-scoop cones, 30% are for two-scoop cones, and the remaining 10% are for three-scoop cones. Recently, the shop added frozen-yogurt cones to its menu. A random sample of 250 frozen yogurt-cone sales revealed the following distribution:
Number of scoops          Number of sales
one                             154
two                             84
three                           12
The owner wishes to know whether the pattern of sales for frozen-yogurt cones differs from that of ice-cream cones. For a goodness-of-fit test based on the χ2 distribution, which of the following is the expected count for the cell corresponding to two scoops?

• 84
• 75
• 83.33

The owner of the ice-cream shop is interested in whether her current ice cream flavors differ in popularity. She has six flavors currently available (chocolate, vanilla, mint chip, coffee, strawberry, and choc chip). Which one of the following pairs of null and alternative hypotheses are appropriate for this test?

• H0: The distribution of the variable “flavor of ice cream” is the same for frozen yogurt cones as it is for ice cream cones.
  Ha: The distribution of the variable “flavor of ice cream” is different for frozen yogurt cones than it is for ice cream cones.
• H0: The observed counts for “flavor of ice cream” are the same for all flavors.
  Ha: At least one of the observed counts for “flavor of ice cream” is different from the corresponding expected count.
• Ho: Flavor preferences for the population are evenly distributed across the six flavors.
  Ha: a. Flavor preferences for the population are not evenly distributed across the six flavors.

From experience, the owner of an ice-cream shop has found that 60% of all sales of ice-cream cone are for one-scoop cones, 30% are for two-scoop cones, and the remaining 10% are for three-scoop cones. Recently, the shop added frozen-yogurt cones to its menu. A random sample of 250 frozen yogurt-cone sales revealed the following distribution:
Number of scoops          Number of sales
one                             154
two                             84
three                           12
The owner wishes to know whether or not the pattern of sales for frozen-yogurt cones differs from that of ice-cream cones and performs a χ2 goodness-of-fit test on the data. which of the following is the correct value of the χ2 statistic?

• 0.2855
• 7.947
• 15.141

A fast-talking salesman offers you a “random digits” smartphone app that comes with a “guarantee” of randomness. You don't trust him, so you insist on testing the app by generating a sample of 100 digits. Here are the resulting frequencies of the ten digits 0 through 9 in your sample of size 100:

• Reject H0 at either the 
  α = 0.05 or α = 0.01
• Reject H0 at α = 0.05 ; fail to reject H0 at α = 0.01
• Fail to reject H0 at either the α = 0.05 or α = 0.01

A survey is given to a sample of male and female adults in which they are asked about their favorite flavor of ice cream.  The totals for each category of response are summarized in the following table:
The expected number of females who prefer vanilla flavor ice cream is...

• (50)(22) / 90
• (40)(22) /90
• 90/[(40)(22)]
• 22/[(40)(90)]

A survey is given to a sample of male and female adults in which they are asked about their favorite flavor of ice cream. They can choose between chocolate, vanilla, and strawberry.

You plan to carry out a chi-square test of homogeneity. Find the degrees of freedom for a X² test of this data:

• 6

• 5

• 2

• 12

A study was done to examine the personal goals of elementary school children. A random sample of 500 students was selected from schools in the state of Georgia. The students received a questionnaire regarding personal goals. They were asked what they would most like to do at school: get good grades, be popular, or be good at sports. The results are presented in the table, classified by the gender of the child.

We wish to test the null hypothesis that gender and personal goal are independent. Which one of the following is the correct χ2 component for the “Boys/Be good at sports” cell?

• 20.010

• 34.504

• 59.496

• 12.665

A student from this sample was selected at random. What is the probability that the student was a girl?

• 0.556
• 0.50
• 278

A student from this sample was selected at random. What is the probability that the student was a girl, given that the student answered "get good grades"?

• 0.578
• 0.694
• 0.668