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Chapter 7: Q.3.3 (page 426)

3. Describe the shape of the

The histogram above left shows the intervals (in minutes) between eruptions of the Old Faithful geyser for all 222recorded eruptions during a particular month. For this population, the median is 75minutes. We used Fathom software to take500SRSs of size 10from the population. The 500values of the sample median are displayed in the histogram above right. The mean of the 500sample median values is 73.5.

Sampling distribution. Explain what this means in terms of overestimating or underestimating the population median

Short Answer

Expert verified

The distribution is unimodal and skewed to the left.

Step by step solution

01

Given Information

Median is75.

Sample size is20.

Mean is73.5

02

Explanation

The figure is

From the figures given above, it is clear that most of the data points are lying on the left side of the graph and it has one peak. Thus, it could be said that the distribution is unimodal and skewed to the left.

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Most popular questions from this chapter

A 10-question multiple-choice exam offers 5choices for each question. Jason just guesses the answers, so he has a probability 1/5of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. One correct way to use a table of random digits to do this is the following:

(a) One digit from the random digit table simulates one answer, with 5=right and all other digits =wrong. Ten digits from the table simulate 10answers. (b) One digit from the random digit table simulates one answer, with 0 or 1 =right and all other digits =wrong. Ten digits from the table simulate 10answers.

(c) One digit from the random digit table simulates one answer, with odd =right and even =wrong. Ten digits from the table simulate 10answers.

(d) Two digits from the random digit table simulate one answer, with 00to 20=right and 21to 99=wrong. Ten pairs of digits from the table simulate 10answers.

(e) Two digits from the random digit table simulate one answer, with 00to 05=right and 06to 99= wrong. Ten pairs of digits from the table simulate 10answers.

How many people are in a car? A study of rush-hour traf铿乧 in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has a mean of 1.5. and a standard deviation of 0.75in the population of all cars that enter this interchange during rush hours.

(a) Could the exact distribution of the count be Normal? Why or why not?

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An agronomist wants to test three different types of fertilizer (A, B, and C) on the yield of a new variety of wheat. The yield will be measured in bushels per acre. Six one-acre plots of land were randomly assigned to each of the three fertilizers. The treatment, experimental unit, and
response variable are, respectively,
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(b) a plot of land, bushels per acre, a specific fertilizer.
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(d) a specific fertilizer, a plot of land, bushels per acre.
(e) a specific fertilizer, the agronomist, bushels per acre

Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must pass through the Customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler鈥檚 luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light shows, the passenger will be searched by Customs agents. A green light means 鈥済o ahead.鈥� Customs agents claim that the proportion of all travelers who will be stopped (red light) is0.30, because the light has probability 0.30of showing red on any push of the button. To test this claim, a concerned citizen watches a random sample of 100travelers push the button. Only 20get a red light.

(a) Assume that the Customs agents鈥� claim is true. Find the probability that the proportion of travelers who get a red light is as small as or smaller than the result in this sample. Show your work.

(b) Based on your results in (a), do you believe the Customs agents鈥� claim? Explain.

A researcher initially plans to take anSRS of size n from a population that has a mean of 80 and a standard deviation of 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied by

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(c) 2.

(d) 12.

(e)12n
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