Question 1

Heights of Adult Males Narrative
The distribution of heights of adult males has a mean of 175.0 cm and a standard deviation of 10.0 cm. A random sample of 36 adult males is selected.
-Refer to Heights of Adult Males Narrative. Find the probability that the average height will be between 171.0 cm and 178.75 cm, inclusively.

Accepted Answer

P(171.0$\le$  $\le$  178.75) = P(-2.40 $\le$  z $\le$ 2.25) = 0.4918 + 0.4878 = 0.9796.

Question 2

Baggage Weights Narrative
The weight of baggage checked by airline passengers is a random variable with a mean of 25 kg and a standard deviation of 12 kg. The total baggage limit for 100 randomly selected passengers is 2740 kg.
-Refer to Baggage Weights Narrative. What is the approximate probability the baggage limit will be exceeded?

Accepted Answer

This is an application of the CLT for the sum of random variables,
P(  >2,740) $\approx$ P(z > 2.5) = 0.0062.

Question 3

Completely describe the sampling distribution of the sample proportion for samples of size n = 500 from a population with p = 0.4.

Accepted Answer

Since np = 200 and n(1 - p) = 300 are both greater than 5, the distribution of the sample proportion  will be approximately normal with a mean  = 0.4 and a standard deviation (or standard error)  = 0.0219.

Question 4

Unemployment Rate Narrative
An eastern province has an unemployment rate of 6%. The province conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.
-Refer to Unemployment Rate Narrative. If Assume the population proportion, p, is unknown. Describe the sampling distribution of  based on the most recent sample.

Accepted Answer

The answer of Unemployment Rate Narrative
An eastern province has an...

Question 5

If the standard error of the sampling distribution of the sample proportion is 0.02049 for samples of size 500, then what may we conclude about the population proportion?

Accepted Answer

A)   The population proportion must be either 0.2 or 0.8.
B)   The population proportion must be either 0.5 or 0.5.
C)   The population proportion must be either 0.3 or 0.7.
D)   The population proportion must be either 0.6 or 0.4.

Question 6

Average Newborn Weights Narrative
It is known that the birth weight of newborn babies in Canada has a mean of 3.20 kg with a standard deviation of 0.80 kg. Suppose we randomly sample 64 birth certificates and record the birth weights of these babies.
-Refer to Average Newborn Weights Narrative. What is the probability the sample mean birth weight as recorded on the birth certificates will be less than 3.125 kg?

Accepted Answer

The answer of Average Newborn Weights Narrative
It is known that...

Question 7

The Central Limit Theorem states that the sampling distribution of the sample mean,  , is approximately normal for large sample sizes (  ).

Accepted Answer

A) True 
 B)False

Question 8

Battery Lifetime Narrative
The lifetime of a particular type of battery is normally distributed with a mean of 1100 days and a standard deviation of 80 days. The manufacturer randomly selects 400 batteries of this type and ships them to a tire retailer.
-Refer to Battery Lifetime Narrative. What is the mean and standard deviation of the sampling distribution of  ?

Accepted Answer

The answer of Battery Lifetime Narrative
The lifetime of a particular...

Question 9

For a  control chart, where are the lower and upper control limits usually set?

Accepted Answer

A)   one standard deviation from the centreline
B)   two standard deviations from the centreline
C)   three standard deviations from the centreline
D)   four standard deviations from the centreline

Question 10

Defective Items Narrative
Suppose a sample of 120 items is drawn from a population of manufactured products and the number of defective items is recorded. Prior experience has shown that the proportion of defectives is 0.05.
-Refer to Defective Items Narrative. What is the likelihood of encountering a sample proportion within  of the population proportion?

Accepted Answer

The answer of Defective Items Narrative
Suppose a sample of 120...

Question 11

Final Exam Scores Narrative
Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 12.
-Refer to Final Exam Scores Narrative. Find the mean and the standard deviation of the sampling distribution of the sample mean  .

Accepted Answer

The answer of Final Exam Scores Narrative
Suppose a random sample...

Question 12

Defective Items Narrative
Suppose a sample of 120 items is drawn from a population of manufactured products and the number of defective items is recorded. Prior experience has shown that the proportion of defectives is 0.05.
-Refer to Defective Items Narrative. Completely describe the sampling distribution of  , the proportion of defectives.

Accepted Answer

The answer of Defective Items Narrative
Suppose a sample of 120...

Question 13

A convenience sample is a sample that can be easily and simply obtained with random selection.

Accepted Answer

A) True 
 B)False

Question 14

The mean of all possible sample proportions  and the expected value of the sampling distribution of  are the same.

Accepted Answer

A) True 
 B)False

Question 15

MRI Accuracy Narrative
A group of medical researchers reported on the accuracy of using magnetic resonance imaging (MRI) to evaluate ligament sprains and tears on 50 patients. Consecutive patients with acute or chronic knee pain were selected from the clinical practice of one of the researchers and agreed to participate in the study.
-Refer to MRI Accuracy Narrative. What chance mechanism could be introduced in order to select a representative sample of 50 individuals with knee pain?

Accepted Answer

The answer of MRI Accuracy Narrative
A group of medical researchers...

Question 16

Rh-Positive Blood Type Narrative
The proportion of individuals with an Rh-positive blood type is 88%. You have a random sample of n = 500 individuals.
-Refer to Rh-Positive Blood Type Narrative. What is the probability that the sample proportion  lies between 86% and 91%?

Accepted Answer

The answer of Rh-Positive Blood Type Narrative
The proportion of individuals...

Question 17

A 1-in-k systematic random sample involves the random selection of one of the first k elements in an ordered population, and then the systematic selection of every kth element thereafter.

Accepted Answer

A) True 
 B)False

Question 18

Twenty-five samples of size 1000 each were drawn from a manufacturing process and the number of defectives in each sample was counted. The average sample proportion was 0.05. What would be the upper control limit for the p chart?

Accepted Answer

A)   0.0206
B)   0.0293
C)   0.0475
D)   0.0707

Question 19

The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the standard deviation of the sampling distribution of the sample mean,  , if a sample of 64 students is selected at random from all students taking that course?

Accepted Answer

A)   10.25
B)   8.00
C)   1.25
D)   1.00

Question 20

A cluster sample is a simple random sample of clusters from the available clusters in the population.

Accepted Answer

A) True 
 B)False

Exam 7: Sampling Distributions

Completely describe the sampling distribution of the sample proportion for samples of size n = 500 from a population with p = 0.4.

If the standard error of the sampling distribution of the sample proportion is 0.02049 for samples of size 500, then what may we conclude about the population proportion?

The Central Limit Theorem states that the sampling distribution of the sample mean, , is approximately normal for large sample sizes ( ).

For a control chart, where are the lower and upper control limits usually set?

A convenience sample is a sample that can be easily and simply obtained with random selection.

The mean of all possible sample proportions and the expected value of the sampling distribution of are the same.

Rh-Positive Blood Type Narrative The proportion of individuals with an Rh-positive blood type is 88%. You have a random sample of n = 500 individuals. -Refer to Rh-Positive Blood Type Narrative. What is the probability that the sample proportion lies between 86% and 91%?

A 1-in-k systematic random sample involves the random selection of one of the first k elements in an ordered population, and then the systematic selection of every kth element thereafter.

Twenty-five samples of size 1000 each were drawn from a manufacturing process and the number of defectives in each sample was counted. The average sample proportion was 0.05. What would be the upper control limit for the p chart?

The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the standard deviation of the sampling distribution of the sample mean, , if a sample of 64 students is selected at random from all students taking that course?

A cluster sample is a simple random sample of clusters from the available clusters in the population.