Deck 10: Confidence Intervals for Means

Question 1

Compute the standard error of a sampling distribution.
Grandma Gertrude's Chocolates, a family owned business, has an opportunity to
Supply its product for distribution through a large coffee house chain. However, the
Coffee house chain has certain specifications regarding cacao content as it wishes to
Advertise the health benefits (antioxidants) of the chocolate products it sells. Suppose
Quality control inspectors at the coffee house chain take a sample of 100 pieces of this
Chocolate product from an incoming shipment. They find a sample average of 60% cacao
With a sample standard deviation of 8%. What is the standard error of the sampling
Distribution of the sample mean?

A) 8%
B) 0.8%
C) 6%
D) 0.6%
E) 0.08%

Answer 1

B

Question 2

Use the Normal to model the distribution of sample means.
A small business ships specialty homemade candies to anywhere in the world. Past
Records indicate that orders weigh an average of 118 grams with a standard deviation of
14 grams. Suppose a random sample of 50 current orders is selected and each weighed
And resulting sample mean is 110 grams. Which of the following statements is true?

A) This sample mean is about 4 standard deviations above what we expect, a very unusual result.
B) This sample mean is less than 3 standard deviations away from the population mean.
C) This sample mean is less than 2 standard deviations away from the population mean.
D) This sample mean is not an unusual result because it is only 8 grams below the population mean.
E) This sample mean is about 4 standard deviations below what we expect, a very

Answer 2

E

Question 3

Use the Normal to model the distribution of sample proportions.
The owner of a small convenience store is trying to decide whether to discontinue
Selling magazines. He suspects that only 5% of the customers buy magazines and thinks
That he might be able to sell something more profitable. Before making a final decision,
He keeps track of the number of customers who buy magazines on a given day. In a
Typical day his store has 280 customers. Which of the following statements is (are) true
About the sampling distribution of the sample proportion of customers who buy specialty
Clothes for their pets at this store?

A) The sampling distribution can be described a Normal model.
B) The mean of the sampling distribution is 0.05.
C) The standard deviation of the sampling distribution is 0.013.
D) All of the above.
E) None of the above.

Answer 3

D

Question 4

Use the Normal to model the distribution of sample means.
In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a
Random sample of 30 rods and measures their lengths. What is the probability of
Observing a sample mean greater than 21 feet?

A) 0.3830
B) 0.8830
C) 0.4778
D) 0.5222
E) 0.1170

Question 5

Compute the standard error of a sampling distribution.
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. However the
Pizza chain has certain specifications regarding the amount of cheese filling in its ravioli.
Suppose quality control inspectors at this pizza restaurant chain sample 100 ravioli from
An incoming shipment. They find a sample average of 16 grams with a standard
Deviation of 1.8 grams. What is the standard error of the sampling distribution of the
Sample mean?

A) 1.8 grams
B) 1.6 grams
C) 0.18 grams
D) 0.16 grams
E) 0.018 grams

Question 6

Use the Normal to model the distribution of sample proportions.
It is generally believed that electrical problems affect about 14% of new cars. An
Automobile mechanic conducts diagnostic tests on 128 new cars on the lot. What is the
Probability that in this group over 18% of the new cars will be found to have electrical
Problems?

A) 0.0985
B) 0.197
C) 0.9015
D) 0.803
E) 0.500

Question 7

Use the Normal to model the distribution of sample means.
A small business ships specialty homemade candies to anywhere in the world. Past
Records indicate that orders weigh an average of 118 grams with a standard deviation of
14 grams. Suppose a random sample of 50 current orders is selected and each weighed
And resulting sample mean is 110 grams. What is the probability of observing a sample
Mean greater than 120 grams?

A) 0.1562
B) 0.8438
C) 0.3438
D) 0.5222
E) 0.1170

Question 8

Use the Normal to model the distribution of sample means.
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on
Data collected from its automatic filling process, the amount of cheese inserted into the
Ravioli is normally distributed with a mean of 15 grams and standard deviation of 0.15
Grams. To make sure that the automatic filling process is on target, quality control
Inspectors take a sample of 25 ravioli and measure the weight of cheese filling. What is
The standard deviation of the sampling distribution of the sample mean weight?

A) 0.006 grams
B) 0.03 grams
C) 0.3 grams
D) 0.06 grams
E) 3 grams

Question 9

Use the Normal to model the distribution of sample proportions.
According to a recent survey, about 33% of Americans polled said that they would
Likely purchase reusable cloth bags for groceries in order to reduce plastic waste.
Suppose 45 shoppers are interviewed a local supermarket. What is the probability that
Between 28% and 38% of shoppers say that they are likely to purchase reusable cloth
Bags for groceries?

A) 0.2389
B) 0.7611
C) 0.4778
D) 0.5222
E) 0.3769

Question 10

Compute the standard error of a sampling distribution.
Automobile mechanics conduct diagnostic tests on 150 new cars of particular make
And model to determine the extent to which they are affected by a recent recall due to
Faulty catalytic converters. They find 28% of the new cars tested do have faulty catalytic
Converters. What is the standard error of the sampling distribution of the sample
Proportion?

A) 0.0013
B) 0.216
C) 0.0056
D) 0.037
E) 0.103

Question 11

Use the Normal to model the distribution of sample means.
In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a
Random sample of 30 rods and measures their lengths. Suppose the resulting sample mean
Is 19.5 feet. Which of the following statements is true?

A) This sample mean is 2.38 standard deviations above what we expect.
B) This sample mean is more than 3 standard deviations away from the population mean.
C) This sample mean is 2.38 standard deviations below what we expect.
D) This sample mean is only 1 standard deviation above the population mean.
E) This sample mean is only 1 standard deviation below the population mean.

Question 12

Apply the Central Limit Theorem.
A small business ships specialty homemade candies to anywhere in the world. Past
Records indicate that orders weigh an average of 118 grams with a standard deviation of
14 grams. Suppose a random sample of 50 current orders is selected and each weighed.
The sampling distribution of the sample mean weights is normally distributed with a
Mean of 118 grams and standard deviation of 1.98. We can say this because

A) the sample size is not too large.
B) the Central Limit theorem applies.
C) the Normal Probability theorem applies.
D) All of the above.
E) None of the above.

Question 13

Use the Normal to model the distribution of sample proportions.
The owner of a pet store is trying to decide whether to discontinue selling specialty
Clothes for pets. She suspects that only 4% of the customers buy specialty clothes for
Their pets and thinks that she might be able to replace the clothes with more profitable
Items. She decides to keep track of the customers who buy specialty clothes for their pets.
If in a typical day there are 275 customers, would be it unusual for her to find that 21
Customers buy these specialty clothes?

A) No, because it is close to the average number expected.
B) No, because it represents 8% of the customers who come to the store on a typical day.
C) Yes, because it is three standard deviations above the mean of the sampling distribution.
D) Yes, because it is two standard deviations below the mean of the sampling distribution.
E) No, because it is less than 4% away from the mean of the sampling distribution.

Question 14

Use the Normal to model the distribution of sample proportions.
According to a recent survey, about 33% of Americans polled said that they would
Likely purchase reusable cloth bags for groceries in order to reduce plastic waste.
Suppose 45 shoppers are interviewed a local supermarket. What is the probability that no
More than 28% of shoppers say that they are likely to purchase reusable cloth bags for
Groceries?

A) 0.2389
B) 0.7611
C) 0.4778
D) 0.5222
E) 0.3769

Question 15

Compute the standard error of a sampling distribution.
A recent survey of 120 senior citizens at a local supermarket found that 44% have
Purchased reusable cloth bags for groceries. What is the standard error of the sampling
Distribution of the sample proportion?

A) 0.0021
B) 0.0453
C) 0.2464
D) 0.0370
E) 0.1030

Question 16

Use the Normal to model the distribution of sample proportions.
The owner of a small convenience store is trying to decide whether to discontinue
Selling magazines. He suspects that only 5% of the customers buy magazines and thinks
That he might be able to sell something more profitable. Before making a final decision,
He keeps track of the number of customers who buy magazines on a given day. In a
Typical day his store has 280 customers. Would it be unusual for 28 customers to
Purchase magazines?

A) No, because it is close to the average number expected.
B) No, because it represents 10% of the customers who come to the store on a typical day.
C) Yes, because it is more than three standard deviations above the mean of the sampling distribution.
D) Yes, because it is two standard deviations below the mean of the sampling distribution.
E) No, because it is only 5% higher than the mean of the sampling distribution.

Question 17

Use the Normal to model the distribution of sample proportions.
It is generally believed that electrical problems affect about 14% of new cars. An
Automobile mechanic conducts diagnostic tests on 128 new cars on the lot. What is the
Probability that in this group between 10% and 18% of the new cars will be found to have
Electrical problems?

A) 0.0985
B) 0.197
C) 0.9015
D) 0.803
E) 0.500

Question 18

Use the Normal to model the distribution of sample means.
Grandma Gertrude's Chocolates, a family owned business, has begun making a new
Line of chocolates with high levels of cacao so it can advertise its health benefits of
Antioxidants. The product with the highest % cacao at Grandma Gertrude's Chocolates
Averages 45% cacao with a standard deviation of 6 %. Suppose a sample of 36 pieces of
This chocolate is taken from the production line. What is the standard deviation of the
Sampling distribution of the sample mean?

A) 1%
B) 0.5%
C) 10%
D) 0.1%
E) 5%

Question 19

Apply the Central Limit Theorem.
In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a
Random sample of 30 rods and measures their lengths. The sampling distribution of the
Sample mean lengths is normally distributed with a mean of 20.5 feet and standard
Deviation of 0.42. We can say this because

A) the sample size is not too large.
B) the Central Limit theorem applies.
C) the Normal Probability theorem applies.
D) All of the above.
E) None of the above.

Question 20

Use the Normal to model the distribution of sample proportions.
The owner of a pet store is trying to decide whether to discontinue selling specialty
Clothes for pets. She suspects that only 4% of the customers buy specialty clothes for
Their pets and thinks that she might be able to replace the clothes with more profitable
Items. In a typical day there are 275 customers. Which of the following statements is
(are) true about the sampling distribution of the sample proportion of customers who buy
Specialty clothes for their pets at this store?

A) The sampling distribution can be described a Normal model.
B) The mean of the sampling distribution is 0.04.
C) The standard deviation of the sampling distribution is 0.012.
D) All of the above.
E) None of the above.