mikaiscute

2022-05-07

An archaeologist has conducted an archaeological surface survey in a region of western New Zealand consisting of a large and fertile valley with a major river flowing down to the coast. The archaeologist has hypothesized that the extremely complex Maori chiefdoms that the Europeans encountered upon contact in the 17th century were relatively recent developments in response to population pressure in the latest prehistoric phase. Further, she has argued that what was once a coastally focused chiefdom oriented towards a maritime economy, became increasingly inland-focused over time, with a subsistence emphasis on root crop agriculture rather than marine resource exploitation in the latest phase.

Sites appear on the surface as large quantities of subsistence debris and lithic artifacts (they had no ceramics), without standing architecture except for readily visible stone ceremonial platforms. The archaeologist has identified two major cultural phases in the region: (1) PHASE I (dated to about A.D. 1000-1300) and (2) PHASE II (dated to about A.D. 1300-1500) from 3 different sites. The archaeologist would like to examine the variable of “population size” in two ways: the absolute size of the site and the number of stone ceremonial platforms. The archaeologist has also reasoned that she can get into the issue of relative reliance on agriculture vs. maritime subsistence by looking at both the distance of sites from the coast and the relative density of fish bones, shell and other marine resources in the surface remains at the site before and after a long period of time. The data collected are as follows:

Site | Period | Size (in ha.) | # Ceremonial Structures | Distance to Coast (in km) | % Marine Resources(before) | % Marine Resources(after) |

1 | 1 | 3.40 | 5.00 | 3.20 | 61.00 | 58.00 |

2 | 1 | 9.80 | 7.00 | 1.20 | 56.00 | 55.00 |

3 | 1 | 4.20 | 6.00 | 3.30 | 54.00 | 52.00 |

1 | 1 | 1.20 | 2.00 | 7.30 | 31.00 | 29.00 |

2 | 1 | 3.30 | 6.00 | 4.40 | 61.00 | 60.00 |

3 | 1 | 2.50 | 4.00 | 5.30 | 45.00 | 45.00 |

1 | 1 | 5.40 | 5.00 | 2.10 | 58.00 | 58.00 |

2 | 1 | 1.60 | 2.00 | 6.80 | 46.00 | 45.00 |

3 | 1 | 2.80 | 5.00 | 5.80 | 47.00 | 46.00 |

1 | 1 | 4.70 | 6.00 | 3.40 | 51.00 | 50.00 |

2 | 1 | 3.60 | 4.00 | 4.40 | 62.00 | 61.00 |

3 | 1 | 9.70 | 3.00 | 2.40 | 53.00 | 53.00 |

1 | 1 | 2.20 | 2.00 | 6.70 | 32.00 | 30.00 |

2 | 1 | 2.80 | 3.00 | 5.20 | 61.00 | 60.00 |

3 | 1 | 2.90 | 4.00 | 4.20 | 67.00 | 66.00 |

1 | 2 | 5.40 | 5.00 | 1.30 | 56.00 | 55.00 |

2 | 2 | 3.30 | 2.00 | 9.30 | 16.00 | 14.00 |

3 | 2 | 9.40 | 6.00 | 7.50 | 32.00 | 30.00 |

1 | 2 | 8.20 | 4.00 | 5.80 | 45.00 | 43.00 |

2 | 2 | 13.40 | 8.00 | 7.80 | 34.00 | 30.00 |

3 | 2 | 2.20 | 2.00 | 8.50 | 26.00 | 25.00 |

1 | 2 | 6.50 | 5.00 | 5.60 | 42.00 | 42.00 |

2 | 2 | 7.30 | 5.00 | 6.30 | 41.00 | 40.00 |

3 | 2 | 4.30 | 4.00 | 8.90 | 24.00 | 23.00 |

1 | 2 | 4.10 | 3.00 | 9.10 | 12.00 | 11.00 |

2 | 2 | 7.10 | 4.00 | 7.10 | 48.00 | 46.00 |

3 | 2 | 9.50 | 6.00 | 7.50 | 36.00 | 35.00 |

1 | 2 | 3.50 | 4.00 | 3.20 | 57.00 | 56.00 |

2 | 2 | 10.30 | 6.00 | 6.20 | 34.00 | 33.00 |

3 | 2 | 2.50 | 3.00 | 4.50 | 46.00 | 46.00 |

1 | 2 | 5.60 | 4.00 | 5.30 | 49.00 | 49.00 |

2 | 2 | 9.10 | 5.00 | 6.50 | 35.00 | 35.00 |

3 | 2 | 9.90 | 7.00 | 7.20 | 22.00 | 22.00 |

1 | 2 | 3.20 | 3.00 | 4.30 | 54.00 | 53.00 |

2 | 2 | 9.20 | 7.00 | 7.10 | 35.00 | 30.00 |

3 | 2 | 5.30 | 5.00 | 8.30 | 32.00 | 32.00 |

1 | 2 | 4.90 | 5.00 | 9.50 | 21.00 | 20.00 |

2 | 2 | 5.10 | 5.00 | 10.20 | 12.00 | 15.00 |

3 | 2 | 6.10 | 6.00 | 8.20 | 23.00 | 23.00 |

1 | 2 | 6.80 | 6.00 | 6.70 | 33.00 | 30.00 |

a. Using the variable “ceremonial structures’, plot a histogram, run the descriptive and interpret the results.

b. Construct a frequency distribution table for the sites and periods then interpret.

c. Construct a 95% Confidence Interval for the variable “distance to coast (in km)” then interpret.

d. Is there a reason to believe that the sample average site size (in ha) is the same as the population site size of 6 ha? Run the appropriate statistical tool and interpret.

e. The archaeologist suspects that the percentage of marine resources decreased after a long period of time. Is there a reason to believe in the archaeologist’s claim?

f. Is there a significant difference in the site size between the two periods?

g. Is there a significant difference in the ceremonial structures between the three different sites?

1. Airline passengers arrive randomly and independently at the passenger-screening facility

at a major international airport. The mean arrival rate is 10 passengers per minute.a) Compute the probability of no arrivals in a one-minute period.

b) Compute the probability that three or fewer passengers arrive in a one-minute period.

c) Compute the probability of no arrivals in a 15-second period.

d) Compute the probability of at least one arrival in a 15-second period.

A young boy asks his mother to get 5 Game-Boy cartridges from his collection of 10 arcade and 5 sports games. How many ways are there that his mother can get 3 arcade and 2 sports games?

1. At a particular factory, every product is inspected by two men. The first inspector catches 80% of the defectives and sends them back for repairs. All the remaining items are sent to a second inspector, who misses about 40% of the defectives that get past the first inspector.

Given that a product was found to be defective, what is the probability that it was found by the first inspector?

(d)

Compute

*P*(*x*≥ 2).*P*(*x*≥ 2) =How do we use computer to generate data?

A coin is tossed

5

times. Find the probability that

none

are

tails.

Let A and B be events with P(A) = 0.8, P(B) = 0.7, and P(A and B) = 0.08. Are A and B

independent?

Suppose x is a random variable with a normal distribution with a mean of 60 and a standard deviation of 5. Find:

a)P(x<65)

b)P(x>53)

A manufacturer claims that at most 20% of the items in a stock are defective.

To test this, 20 items are randomly selected from the product.

If at most 3 items are defective, then the manufacturer is statement is accepted.

If the true probability of an item being defective is 0.2.

Find the probability of accepting the manufacturer’s statement?

(Hint: use the Binomial Distribution)

When not interrupted artificially, the duration of human pregnancies can be described, we will assume, by a mean of nine months (270 days) and a standard deviation of one-half month (15 days).

Between what two times, in days, will a majority of babies arrive?

The probability of a randomly selected adult in one country being infected with a certain virus is

0.006.

In tests for the virus, blood samples from

11

people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.

Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value

tα/2,

(b) find the critical value

zα/2,

or (c) state that neither the normal distribution nor the t distribution applies.

Here are summary statistics for randomly selected weights of newborn girls:

n=277,

x=28.5

hg,

s=6.8

hg. The confidence level is

95%.

Consider all seven-digit numbers that can be created from the digits 0-9$0\text{-}9$ where the first and last digits must be even and no digit can repeat. Assume that numbers can start with 0$0$. What is the probability of choosing a random number that starts with 8$8$ from this group?