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Chapter 7: Q. 8 (page 454)

Sample minimums List all 10possible SRSs of size n=3, calculate the minimum quiz score for each sample, and display the sampling distribution of the sample minimum on a dotplot.

Short Answer

Expert verified

The minimum sampling :

Sample of size 3
Sample Mean
Abigail - Bobby - Carlos
5
Abigail - Bobby - DeAnna
5
Abigail - Bobby - emily
5
Abigail - Carlos - DeAnna
7
Abigail - Carlos - Emily
9
Abigail - DeAnna - Emily
7
Bobby - Carlos - DeAnna
5
Bobby - Carlos - Emily
5
Bobby - DeAnna - Emily
5
Carlos - DeAnna - Emily
7

The dotplot is given below:

Step by step solution

01

Given information

We need to find minimum quiz score for each sample, and display the sampling distribution of the sample minimum on a dotplot for given table

Name
Gender
Quiz score
Abigail
Female
10
Bobby
Male
5
Carlos
Male
10
DeAnna
Female
7
Emily
Female
9
02

Simplify

As we know sample mean is minimum of the quiz score of sample.

Now, n=3, therefore,

Sample of size 3
Sample mean
Abigail - Bobby -Carlos
Min(10,5,10)=5
Abigail - Bobby - DeAnna
Min(10,5,7)=5
Abigail - Bobby - Emily
Min(10,5,9)=5
Abigail - Carlos - DeAnna
Min(10,10,7)=7
Abigail - Carlos - Emily
Min(10,10,9)=9
Abigail - DeAnna - Emily
Min(10,7,9)=7
Bobby - Carlos - DeAnna
Min(5,10,7)=5
Bobby - Carlos - Emily
Min(5,10,9)=5
Bobby - DeAnna - Emily
Min(5,7,9)=5
Carlos - DeAnna - Emily
Min(10,7,9)=7

A dot plot is a graph that shows the distribution of numerical variables by using dots to represent values.
If a value appears more than once in a whole number, the dots are stacked one on top of the other, with the height of the column of dots representing the frequency of that value.

Now from the above table, dot plot will be :

From dot plot,

Centre is about 8.25

Minimum =6

Maximum =10

Range =4

The distribution is slightly negative of left skewed.

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Most popular questions from this chapter

The distribution of scores on the mathematics part of the SAT exam in a recent year was approximately Normal with mean 515 and standard deviation 114 . Imagine choosing many SRSs of 100 students who took the exam and averaging their SAT Math scores. Which of the following are the mean and standard deviation of the sampling distribution of x-?x炉?

a. Mean =515,SD=114

b. Mean =515,SD=114/100SD=114/100

c. Mean role="math" localid="1654342976765" =515/100,SD=114/100

d. Mean role="math" localid="1654343050312" =515/100,SD=114/100SD=114/10

e. Cannot be determined without knowing the 100 scores.

Warm turkey Tom is cooking a large turkey breast for a holiday meal. He wants to be sure that the turkey is safe to eat, which requires a minimum internal temperature of 165掳FTom uses a thermometer to measure the temperature of the turkey meat at four randomly chosen points. The minimum reading is 170掳F

identify the population, the parameter, the sample, and the statistic.

The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the

a. sample size is reasonably large (for any population).

b. population is Normally distributed (for any sample size).

c. population is Normally distributed and the sample size is reasonably large.

d. population is Normally distributed and the population standard deviation is known (for any sample size).

e. population size is reasonably large (whether the population distribution is known or not).

Suppose we select an SRS of size n=100n=100from a large population having proportion p of successes. Let p鈭�p^be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p鈭�p^?

a. 0.01

b. 0.09

c. 0.85

d. 0.975

e. 0.999

In a residential neighborhood, the median value of a house is \(200,000. For which of the

following sample sizes is the sample median most likely to be above \)250,000?

(a) n=10n=10

(b) n=50n=50

(c) n=100n=100

(d) n=1000n=1000

(e) Impossible to determine without more information.
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