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Chapter 8: Q.30 (page 496)

Whelks and mussels The small round holes you often see in sea shells were drilled by other sea creatures, who ate the former dwellers of the shells. Whelks often drill into mussels, but this behavior appears to be more or less common in different locations. Researchers collected whelk eggs from the coast of Oregon, raised the whelks in the laboratory, then put each whelk in a container with some delicious mussels. Only 9of98whelks drilled into a mussel. The researchers want to estimate the proportion p of Oregon whelks that will spontaneously drill into mussels.

Short Answer

Expert verified

All three conditions for confidence interval is not satisfied.

Step by step solution

01

Step-1 Given Information 

Given in the question that ,

Number of success=9The researchers want to estimate the proportion pof Oregon whelks that will spontaneously drill into mussels.

02

Step-2 Explanation

To calculate a confidence interval three conditions should be satisfied. The conditions are Random, Independent and Normal.

The condition of random is unknown in the description. Thus, random is not satisfied.

Since the sample size is less than 10%of the population size thus the condition of independent is satisfied.

The survey results the number of success is 9is less than 10thus condition of normal is not satisfied.

Hence, all three conditions for confidence interval is not satisfied.

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Most popular questions from this chapter

98% Confidence find z*for a98%confidence interval using table A or tour calculator. show your method.

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24laboratory rats. A 95%confidence interval for the mean blood cholesterol level Mis 80.2to 89.8. Which of the following would cause the most worry about the validity of this interval?

(a) There is a clear outlier in the data.

(b) A stemplot of the data shows a mild right skew.

(c) You do not know the population standard deviation S.

(d) The population distribution is not exactly Normal.

(e) None of these would be a problem because the t procedures are robust.

5. NAEP scores Young people have a better chance of full-time employment and good wages if they are good with numbers. How strong are the quantitative skills of young Americans of working age? One source
of data is the National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey, which is based on a nationwide probability sample of households. The NAEP survey includes a
short test of quantitative skills, covering mainly basic arithmetic and the ability to apply it to realistic problems. Scores on the test range from 0to 500. For example, a person who scores 233can add the amounts of two checks appearing on a bank deposit slip; someone scoring 325can determine the price of a meal from a menu; a person scoring 375 can
transform a price in cents per ounce into dollars per pound. Suppose that you give the NAEP test to an SRS of 840people from a large population in which the scores have mean 280and standard deviation蟽=60. The mean xof the 840 scores will vary if you take repeated samples.
(a) Describe the shape, center, and spread of the sampling distribution of x.
(b) Sketch the sampling distribution of x. Mark its mean and the values one, two, and three standard deviations on either side of the mean.
(c) According to the68鈥�95鈥�99.7rule, about 95%of all values of x炉lie within a distance mof the mean of the sampling distribution. What is m? Shade the region on the axis of your sketch that is within m of the mean.

(d) Whenever x炉falls in the region you shaded, the population mean 渭lies in the confidence intervalx卤m. For what percent of all possible samples does the interval capture 渭?

63. Give it some gas! Computers in some vehicles calculate various quantities related to performance. One of these is fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle
equipped in this way, the miles per gallon were recorded each time the gas tank was filled and the computer was then reset. Here are the mpg values for a random sample of 20of these records:

15.813.615.619.122.415.622.517.219.422.6
19.418.014.618.721.014.822.621.514.320.9
Construct and interpret a 95% confidence interval for the mean fuel efficiency M for this vehicle.

Exercises 53 and 54 refer to the following setting. The table below displays the number of accidents at a factory during each hour of a 24-hour shift (1  1 a.m).

53. Accidents happen (1.2, 3.1)
(a) Construct a plot that displays the distribution of the number of accidents effectively.
(b) Construct a plot that shows the relationship between the number of accidents and the time when they occurred.
(c) Describe something that the plot in part (a) tells you about the data that the plot in part (b) does not.
(d) Describe something that the plot in part (b) tells you about the data that the plot in part (a) does not.
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