Deck 7: Hypothesis Testing With One Sample

Question 1

For the next questions, test the given claim using the traditional method for
hypothesis testing about a standard deviation. Assume that a simple random
sample has been taken and the population is normally distributed.
Health care administrators at Atlanta area hospitals are investigating whether the quality
of care given to pneumonia patients varies less than the United States hospital
population standard deviation of 16. From a sample of nine Atlanta area hospitals, they
found the portion of pneumonia patients who were given initial antibiotics within the
first four minutes of arrival had a standard deviation of 10. Use a .05 significance level
to test the claim that Atlanta area hospitals have less variation in the quality of care
given to pneumonia patients than United States hospitals.
Identify the test statistic.

Answer 1

Test statistic for

Question 2

Identify the Type I error.
The standard deviation of the diameter at breast height, or DBH, of the slash pine tree is less than one inch.

A) Fail to support the claim when is true.
B) Support the claim when is true.
C) Support the claim when is true.
D) Fail to support the claim when is true.

Answer 2

Support the claim when is true.

Question 3

Find the critical value z assuming application of a normal distribution.
Left-tailed test; Find the value of the test statistic z using the following information.

Answer 3

Question 4

For the next questions, test the given claim using the traditional method for
hypothesis testing about a standard deviation. Assume that a simple random
sample has been taken and the population is normally distributed.
Health care administrators at Atlanta area hospitals are investigating whether the quality
of care given to pneumonia patients varies less than the United States hospital
population standard deviation of 16. From a sample of nine Atlanta area hospitals, they
found the portion of pneumonia patients who were given initial antibiotics within the
first four minutes of arrival had a standard deviation of 10. Use a .05 significance level
to test the claim that Atlanta area hospitals have less variation in the quality of care
given to pneumonia patients than United States hospitals.
Identify the critical value(s).

Question 5

Determine which is the appropriate approach to conduct a hypothesis test.
Claim: The mean RDA of sodium is 2400mg. Sample data: , s = 550 . The sample data appear to come from a normally distributed population.

A) Use the normal distribution.
B) Use the Student t distribution.
C) Use the Chi square distribution.
D) Use nonparametric or bootstrapping methods.

Question 6

For the next questions, test the given claim using the P-value method for
hypothesis testing about a proportion. Assume a simple random sample has been
taken, the conditions for a binomial distribution are satisfied, and the sample
proportions can be approximated by a normal distribution.
In order to track the percentage of misdiagnoses by Emergency Room doctors, a sample
of 900 patients revealed that 45 patients were misdiagnosed with indigestion instead of
a heart attack. Test the claim that physicians misdiagnose less than 6% of heart attacks.
Use a .01 significance level.
Identify the P-value and level of significance.

Question 7

For the next questions, test the given claim using the P-value method for
hypothesis testing about a proportion. Assume a simple random sample has been
taken, the conditions for a binomial distribution are satisfied, and the sample
proportions can be approximated by a normal distribution.
In order to track the percentage of misdiagnoses by Emergency Room doctors, a sample
of 900 patients revealed that 45 patients were misdiagnosed with indigestion instead of
a heart attack. Test the claim that physicians misdiagnose less than 6% of heart attacks.
Use a .01 significance level.
Identify the null hypothesis and alternative hypothesis.

Question 8

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume a simple random sample has been taken,
the population standard deviation is known, and the population is normally
distributed.
At a dam in Oregon, fisheries biologists are studying the length of the pikeminnow fish
to investigate the population structure of resident fish. They collect a sample of 60
pikeminnow and find that the mean length is 15 inches. Assume the population standard
deviation is known from a previous study to be 1.5 inches. Use a .05 significance level
to test the claim that the pikeminnow have a mean length greater than 14 inches.
Identify the null hypothesis and alternative hypothesis.

Question 9

For the next questions, find the P-value using the given information
With .

Question 10

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume that a simple random sample has been
taken, the population standard deviation is not known, and the population is
normally distributed.
The Common Murre population of birds became endangered in California due to an oil
spill. Biologists want to know if their efforts to restore the colony have been successful.
Since the breeding colony of birds is site dependent, the mean number of breeding pairs
of Common Murres were observed at a specific rock known to be a breeding site. Test
the claim that the mean number of breeding pairs of the Common Murre is greater than
400. Use a .05 significance level and the following raw data collected from seven days
of observations:
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 11

For the next questions, test the given claim using the traditional method for
hypothesis testing about a standard deviation. Assume that a simple random
sample has been taken and the population is normally distributed.
Health care administrators at Atlanta area hospitals are investigating whether the quality
of care given to pneumonia patients varies less than the United States hospital
population standard deviation of 16. From a sample of nine Atlanta area hospitals, they
found the portion of pneumonia patients who were given initial antibiotics within the
first four minutes of arrival had a standard deviation of 10. Use a .05 significance level
to test the claim that Atlanta area hospitals have less variation in the quality of care
given to pneumonia patients than United States hospitals.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 12

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume that a simple random sample has been
taken, the population standard deviation is not known, and the population is
normally distributed.
The Common Murre population of birds became endangered in California due to an oil
spill. Biologists want to know if their efforts to restore the colony have been successful.
Since the breeding colony of birds is site dependent, the mean number of breeding pairs
of Common Murres were observed at a specific rock known to be a breeding site. Test
the claim that the mean number of breeding pairs of the Common Murre is greater than
400. Use a .05 significance level and the following raw data collected from seven days
of observations:
Identify the null hypothesis and alternative hypothesis.

Question 13

For the next questions, find the P-value using the given information
With .

Question 14

Find the critical value z assuming application of a normal distribution.
In a lawsuit challenging Kraft Foods, General Mills, and Kellogg, a consumer alleges that they are misrepresenting the nutritional advantages of "low sugar" cereals. The suit states that although the amount of sugar in their "low sugar" cereals is reduced, the total amount of carbohydrates has not been reduced. The claim states that the mean amount of total carbohydrates in the "low sugar" cereals is equal to 25 grams. Find the critical value z assuming application of a normal distribution.

Question 15

For the next questions, test the given claim using the P-value method for
hypothesis testing about a proportion. Assume a simple random sample has been
taken, the conditions for a binomial distribution are satisfied, and the sample
proportions can be approximated by a normal distribution.
In order to track the percentage of misdiagnoses by Emergency Room doctors, a sample
of 900 patients revealed that 45 patients were misdiagnosed with indigestion instead of
a heart attack. Test the claim that physicians misdiagnose less than 6% of heart attacks.
Use a .01 significance level.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 16

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume that a simple random sample has been
taken, the population standard deviation is not known, and the population is
normally distributed.
The Common Murre population of birds became endangered in California due to an oil
spill. Biologists want to know if their efforts to restore the colony have been successful.
Since the breeding colony of birds is site dependent, the mean number of breeding pairs
of Common Murres were observed at a specific rock known to be a breeding site. Test
the claim that the mean number of breeding pairs of the Common Murre is greater than
400. Use a .05 significance level and the following raw data collected from seven days
of observations:
Identify the P-value and level of significance.

Question 17

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume a simple random sample has been taken,
the population standard deviation is known, and the population is normally
distributed.
At a dam in Oregon, fisheries biologists are studying the length of the pikeminnow fish
to investigate the population structure of resident fish. They collect a sample of 60
pikeminnow and find that the mean length is 15 inches. Assume the population standard
deviation is known from a previous study to be 1.5 inches. Use a .05 significance level
to test the claim that the pikeminnow have a mean length greater than 14 inches.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 18

For the next questions, find the P-value using the given information
For the next four years, medical researchers are following 4,500 randomly selected healthy women who have a high risk of developing breast cancer. The study of women in the U.S., Canada, and Spain is to examine whether Aromasin, a drug made by Pfizer, can prevent breast cancer. They claim that the proportion of women taking Aromasin who develop breast cancer will be less than 33%. Find the critical value z assuming application of a normal distribution.

Question 19

For the next questions, test the given claim using the traditional method for
hypothesis testing about a standard deviation. Assume that a simple random
sample has been taken and the population is normally distributed.
Health care administrators at Atlanta area hospitals are investigating whether the quality
of care given to pneumonia patients varies less than the United States hospital
population standard deviation of 16. From a sample of nine Atlanta area hospitals, they
found the portion of pneumonia patients who were given initial antibiotics within the
first four minutes of arrival had a standard deviation of 10. Use a .05 significance level
to test the claim that Atlanta area hospitals have less variation in the quality of care
given to pneumonia patients than United States hospitals.
Identify the null hypothesis and alternative hypothesis.

Question 20

Find the value of the test statistic z using the following information.
An environmental non-profit group collected a sample of 200 juvenile salmon from a created wetland to test whether the population of fish is eating less than 40% Chironomids, a type of fly. After flushing the contents of the stomachs, they find that the sample of juvenile salmon is eating 38% Chironomids. For the next two questions, find the P-value using the given information.

Question 21

For the next questions, find the P-value using the given information
Right-tailed test;

Question 22

For the next questions, find the P-value using the given information
With

Question 23

Identify the Type I error.
The EPA claims that fluoride in children's drinking water should be at a mean level of less than 1.2 ppm, or parts per million, to reduce the number of dental cavities.

A) Fail to support the claim when is true.
B) Support the claim when is true.
C) Support the claim when is true.
D) Fail to support the claim when is true.

Question 24

Determine which is the appropriate approach to conduct a hypothesis test.
Claim: The AI, or Adequate Intake of water, for pregnant women is a mean of 3L/d, liters per day. Sample data: n = 200 , X = 2.5 , s =1. The sample data appear to come from a normally distributed population with σ=1.2 .

A) Use the normal distribution.
B) Use the Student t distribution.
C) Use the Chi square distribution.
D) Use nonparametric or bootstrapping methods.

Question 25

For the next questions, test the given claim using the traditional method for
hypothesis testing about a standard deviation. Assume that a simple random
sample has been taken and the population is normally distributed.
According to the U.S. Department of Agriculture, imports of Canadian grown potatoes
have depressed U.S. sales of potatoes during the last six years. From this sample, the
standard deviation is 2.07. Assume we know from the past, the population standard
deviation of sales was .79. Use a .05 significance level to test the claim that U.S. potato
sales have more variation in the last six years than in the past.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 26

For the next questions, test the given claim using the P-value method for
hypothesis testing about a proportion. Assume a simple random sample has been
taken, the conditions for a binomial distribution are satisfied, and the sample
proportions can be approximated by a normal distribution.
In order to evaluate patient response to a course of therapy to treat brain tumors, a
sample of 300 patients revealed that 96 patients were responsive to a certain course of
treatment. Test the claim that more than 30% of patients with brain tumors were
responsive to treatment. Use a .01 significance level.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 27

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume a simple random sample has been taken,
the population standard deviation is known, and the population is normally
distributed.
Medical researchers evaluating a drug for Multiple Sclerosis found in a sample of 500
patients that the mean number of relapses was 165. Assume the population standard
deviation is known from a previous study to be 50. Use a .05 significance level to test
the claim that the drug has a mean number of relapses less than 170.
Identify the null hypothesis and alternative hypothesis.

Question 28

For the next questions, find the P-value using the given information
With

Question 29

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume that a simple random sample has been
taken, the population standard deviation is not known, and the population is
normally distributed.
Biologists are investigating if their efforts to prevent erosion on the bank of a stream
have been statistically significant. For this stream, a narrow channel width is a good
indicator that erosion is not occurring. Test the claim that the mean width of ten
locations within the stream is more than 3.7 meters. Use a .05 significance level and the
following sample data:
Identify the P-value and level of significance.

Question 30

For the next questions, test the given claim using the traditional method for
hypothesis testing about a standard deviation. Assume that a simple random
sample has been taken and the population is normally distributed.
According to the U.S. Department of Agriculture, imports of Canadian grown potatoes
have depressed U.S. sales of potatoes during the last six years. From this sample, the
standard deviation is 2.07. Assume we know from the past, the population standard
deviation of sales was .79. Use a .05 significance level to test the claim that U.S. potato
sales have more variation in the last six years than in the past.
Identify the null hypothesis and alternative hypothesis.

Question 31

For the next questions, test the given claim using the P-value method for
hypothesis testing about a proportion. Assume a simple random sample has been
taken, the conditions for a binomial distribution are satisfied, and the sample
proportions can be approximated by a normal distribution.
In order to evaluate patient response to a course of therapy to treat brain tumors, a
sample of 300 patients revealed that 96 patients were responsive to a certain course of
treatment. Test the claim that more than 30% of patients with brain tumors were
responsive to treatment. Use a .01 significance level.
Identify the null hypothesis and alternative hypothesis.

Question 32

For the next questions, test the given claim using the traditional method for
hypothesis testing about a standard deviation. Assume that a simple random
sample has been taken and the population is normally distributed.
According to the U.S. Department of Agriculture, imports of Canadian grown potatoes
have depressed U.S. sales of potatoes during the last six years. From this sample, the
standard deviation is 2.07. Assume we know from the past, the population standard
deviation of sales was .79. Use a .05 significance level to test the claim that U.S. potato
sales have more variation in the last six years than in the past.
Identify the test statistic.

Question 33

For the next questions, test the given claim using the P-value method for
hypothesis testing about a proportion. Assume a simple random sample has been
taken, the conditions for a binomial distribution are satisfied, and the sample
proportions can be approximated by a normal distribution.
In order to evaluate patient response to a course of therapy to treat brain tumors, a
sample of 300 patients revealed that 96 patients were responsive to a certain course of
treatment. Test the claim that more than 30% of patients with brain tumors were
responsive to treatment. Use a .01 significance level.
Identify the P-value and level of significance.

Question 34

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume that a simple random sample has been
taken, the population standard deviation is not known, and the population is
normally distributed.
Biologists are investigating if their efforts to prevent erosion on the bank of a stream
have been statistically significant. For this stream, a narrow channel width is a good
indicator that erosion is not occurring. Test the claim that the mean width of ten
locations within the stream is more than 3.7 meters. Use a .05 significance level and the
following sample data:
Identify the null hypothesis and alternative hypothesis.

Question 35

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume that a simple random sample has been
taken, the population standard deviation is not known, and the population is
normally distributed.
Biologists are investigating if their efforts to prevent erosion on the bank of a stream
have been statistically significant. For this stream, a narrow channel width is a good
indicator that erosion is not occurring. Test the claim that the mean width of ten
locations within the stream is more than 3.7 meters. Use a .05 significance level and the
following sample data:
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 36

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume a simple random sample has been taken,
the population standard deviation is known, and the population is normally
distributed.
Medical researchers evaluating a drug for Multiple Sclerosis found in a sample of 500
patients that the mean number of relapses was 165. Assume the population standard
deviation is known from a previous study to be 50. Use a .05 significance level to test
the claim that the drug has a mean number of relapses less than 170.
Identify the P-value and level of significance.

Question 37

For the next questions, test the given claim using the P-value method for
hypothesis testing about a mean. Assume a simple random sample has been taken,
the population standard deviation is known, and the population is normally
distributed.
Medical researchers evaluating a drug for Multiple Sclerosis found in a sample of 500
patients that the mean number of relapses was 165. Assume the population standard
deviation is known from a previous study to be 50. Use a .05 significance level to test
the claim that the drug has a mean number of relapses less than 170.
State a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

Question 38

For the next questions, find the P-value using the given information
Biologists studying the tropical reestablishment of bursera simaruba, the gumbo- limbo tree, monitored the survival of a sample of 90 trees to determine if the population survival rate was greater than 35%. After five months, the survival rate of the trees was 45%. For the next two questions, find the P-value using the given information.

Question 39

For the next questions, test the given claim using the traditional method for
hypothesis testing about a standard deviation. Assume that a simple random
sample has been taken and the population is normally distributed.
According to the U.S. Department of Agriculture, imports of Canadian grown potatoes
have depressed U.S. sales of potatoes during the last six years. From this sample, the
standard deviation is 2.07. Assume we know from the past, the population standard
deviation of sales was .79. Use a .05 significance level to test the claim that U.S. potato
sales have more variation in the last six years than in the past.
Identify the critical value(s).