Mathematics

**Salaries of postgraduates**

The *Economics of Education Review* (Vol. 21, 2002) published a paper on the relationship between education level and earnings. The date for the research were obtained from the National Adult Literacy Survey of more than 25,000 respondents. The survey revealed that males with a postgraduate degree have a mean salary of $61,340 (with standard error *Sx̄* = $2,185), while females with a postgraduate degree have a mean of $32,227 (with standard error *Sx̄* = $932).

**Questions**

1. The article reports that a 95% confidence interval for *μ*_{M}, the population mean salary of all males with postgraduate degree, is ($57,050, $65,631). Based on this interval, is there evidence to say that *μ*_{M} differs from $60,000? Explain.

2. Use the 5-step process to test the hypothesis that the true mean salary of males with postgraduate degree differs from $60,000. Use *α *= .50.

**Judgment**

The authors of an article within the *Journal of Marketing Research* (Dec. 2011) study grocery store shopper’ judgments. For one part of the study, 11 consumers were told to put their arm in a flex position (similar to a shopping basket) and then each consumer was offered several choices between a vice product and a virtue product (e.g., a movie ticket vs. a shopping coupon, pay later with a larger amount vs. pay now). Based on these choices, a vice choice score was determined on a scale of 0 to 100 (where higher scores indicate a greater preference for vice options). The data in the table are (simulated) choice scores for the 11 consumers. Suppose that the average choice score for consumers with an extended arm position (similar to pushing a shopping cart) is known to be *μ*= 50. The researchers theorize that the mean choice score for consumers shopping with a flexed arm will be higher than 43 (reflecting their higher propensity to select a vice product.)

**Question**

Using the 5-step process, test this hypothesis at *α*= .05.

**Organic–certified coffee**

Coffee markets that conform to organic standards focus on the environmental aspects of coffee growing, such as the use of shade trees and reduced reliance on chemical pesticides. A study of organic coffee growers was published in *Food Policy* (Vol. 36, 2010). In a representative sample of 845 coffee growers from southern Mexico, 417 growers were certified to sell to organic coffee markets while 77 growers were transitioning to become organic certified. In the United States, 60% of coffee growers are organic certified.

**Question**

Is there evidence to indicate that fewer than 60% of the coffee growers in southern Mexico are either organic certified or transitioning to become organic certified? Use the 5-step process for hypothesis testing and calculate the probability of a Type I error.

**Fingerprint expertise**

Refer to the *Psychological Science* (August 2011) study of fingerprint identification. The study found that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. In contrast, a novice will correctly identify the match 75% of the time. Consider a sample of five different parts of fingerprints, where each pair is a match.

**Questions**

1. What is the probability that an expert will correctly identify the match in all five pairs of fingerprints?

2. What is the probability that a novice will correctly identify the match in all five pairs of fingerprints?

**Airline fatalities**

U.S. airlines average about 4.5 fatalities per month (*Statistics Abstract of the United States*: 2012). Assume the probability distribution for *x*, the number of fatalities per month, can be approximated by a Poisson probability distribution.

1. Find *E* (*x*) and the standard deviation of *x*.

Below is the data needed for question titled “Judgement”

Problem #5 |

CHOICE |

56 |

76 |

62 |

57 |

55 |

61 |

62 |

43 |

57 |

61 |

58 |

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