Statistics Exam: Sampling Distributions and Estimation, Exams of Nursing

A statistics exam focused on sampling distributions and estimation techniques. It includes problems related to approximating sampling distributions with normal probability distributions, determining appropriate sample sizes for estimating population parameters, and calculating probabilities related to sample means. Each problem is accompanied by a detailed answer key, providing step-by-step solutions and explanations. The exam covers key concepts such as the central limit theorem, standard deviation, and z-scores, offering valuable practice for students studying introductory statistics. It also includes instructor comments on one of the answers.

Typology: Exams

2025/2026

Available from 12/31/2025

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MATH 110 - Introduction
to Statistics Module 5
Exam
Exam Page 1
Suppose that you take a sample of size 50 from a population that is not normally
distributed. Can the sampling distribu
ti
on of
x
be approximated by a normal
probability distribu
ti
on?
Yes, the sample size can be approximated by a normal probablity ditribution
because the sample size is greater than 30.
Answer Key
Suppose that you take a sample of size 50 from a population that is
not normally distributed. Can the sampling distribu
ti
on of
x
be
approximated by a normal probability distribu
ti
on?
Yes. The sample size is greater than 30, therefore, we may
approximate by a normal probability distribution.
pf3
pf4
pf5

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MATH 110 - Introduction to Statistics Module 5 Exam Exam Page 1 Suppose that you take a sample of size 50 from a population that is not normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution? Yes, the sample size can be approximated by a normal probablity ditribution because the sample size is greater than 30.

Answer Key

Suppose that you take a sample of size 50 from a population that is

not normally distributed. Can the sampling distribution of x̄ be

approximated by a normal probability distribution?

Yes. The sample size is greater than 30, therefore, we may

approximate by a normal probability distribution.

Exam page 3

Suppose that you are attempting to estimate the annual income of

1200 families. In order to use the infinite standard deviation

formula, what sample size, n, should you use?

(n / N ) ≤0.

N = 1200

n ≤ (0.05 x 1200 ) = 60 n ≤ 60 The sample size (n) has to be less than or equal to 60 n ≤ 60 The sample size (n) has to be less than or equal to 60

Answer Key

Suppose that you are attempting to estimate the annual income of

1200 families. In order to use the infinite standard deviation

formula, what sample size, n, should you use?

In order to use infinite standard deviation formula, we should have:

n≤0.05(1200)

n≤

So, the sample size should be less than 60.

that a simple random sample of 30 nurses will have a mean time of

150 seconds or less.

Exam Page 4 Suppose that in a very large city 9.8 % of the people have more than two jobs. Suppose that you take a random sample of 70 people in that city, what is the probability that 9 % or more of the 70 have more than two jobs? We want P(Z>-0.23). From the standard normal table, we find: P(Z>-.23)=1- P(Z<-.23)=1-.40905=.59095. So there is a .60257 probability that the percentage of the sample that have more than two jobs is more than 9 %. -1.0 points Instructor Comments The value stated in the conclusion is not correct.

Answer Key

Suppose that in a very large city 9.8 % of the people have

more than two jobs. Suppose that you take a random

sample of 70 people in that city, what is the probability

that 9 % or more of the 70 have more than two jobs?

Now we find the z-score:

We want P(Z>-0.23). From the standard

normal table, we find: P(Z>-.23)=1-

P(Z<-.23)=1-.40905=.59095.

So there is a .60257 probability that the percentage of

the sample that have more than two jobs is more than 9