review stats test 3
The target temperature for a hot beverage the moment it is dispensed from a vending machine is 170°F. A consumer organization believes that a particular brand of machine dispenses beverages whose temperature exceeds 170°F. In this scenario, a Type 2 error would be: (a) Deciding that the beverages do not exceed 170°F when they do. (b) Deciding that the beverages exceed 170°F when they don't.
(a)
A sociologist wishes to test H0: µ =42 vs. Ha: µ ≠42. The sociologist takes a sample of size 100 and calculates a standardized test statistic of -2.34. To calculate a p-value for the test in Excel, the sociologist should use:
2*NORM.DIST(-2.34,0,1,TRUE)
A veterinarian reads that 15% of dogs are allergic to chicken. However, he claims that the actual proportion is less than this. He randomly selects 15 of his customers and asks them if their dog is allergic to chicken. 3 of them say yes. Assume the population is normally distributed and use a=0.01. Which function in Excel finds the test statistic? (Note 3/15 =0.20)
=(0.20-0.15)/SQRT(0.15*0.85/15)
A veterinarian reads that 15% of dogs are allergic to chicken. However, he claims that the actual proportion is less than this. He randomly selects 15 of his customers and asks them if their dog is allergic to chicken. 3 of them say yes. Assume the population is normally distributed and use 𝛼=0.01α=0.01. Which function in Excel finds the test statistic? (Note: 3/15 = 0.20)
=(0.20-0.15)/SQRT(0.15*0.85/15)
A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use a = 0.05 to test the claim. Which function in Excel finds the test statistic?
=(250-300)/(10/SQRT(25))
A nutritionist claims that the average amount of sugar in a 16 oz soda is at least 50 g. He randomly samples 10 sodas and finds they contain an average of 54 g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use 𝛼=0.10α=0.10to test the claim. Which function in Excel finds the test statistic?
=(54-50)/(3/SQRT(10))
A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5,912 with a standard deviation of $300. Use a=0.05 to test the claim. Which function in excel finds the test statistic?
=(5705-5912)/(300/SQRT(100))
An english professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds that the average amount of semicolons is 8.5. Assume the population is normally distributed and use a=0.05 to test the claim. Which formula in Excel finds the test statistic?
=(8.5-8)-(2/SQRT(25))
An english professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds that the average amount of semicolons is 8.5. Assume the population is normally distributed and use a=0.05 to test the claim. Which formula in excel finds the test statistic?
=(8.5-8)-(2/SQRT(25))
An English professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds the average amount of semicolons is 8.5. Assume the population is normally distributed and use 𝛼=0.05α=0.05to test the claim. Also suppose that the test statistic equals 0.85. Which formula in Excel finds the p-value?
=1-NORM.DIST(0.85, 0, 1, TRUE)
A sociologist wishes to test H0: µ =42 vs. Ha: µ >42. The sociologist takes a sample of size 100 and calculates a standardized test statistic of 2.34. To calculate a p-value for the test in Excel, the sociologist should use:
=1-NORM.DIST(2.34,0,1,TRUE)
A sociologist wishes to test H0: µ =42 vs. Ha: µ >42. The sociologist takes a sample of size 10 and calculates a standardized test statistic of 2.34. To calculate a p-value for the test in Excel, the sociologist should use:
=1-T.DIST(2.34,9,TRUE)
A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5,912 with a standard deviation of $300. Use a=0.05 to test the claim. Suppose the test statistic is 1.65 Which function in Excel finds the p-value?
=2*NORM.DIST(-1.65,0,1,TRUE)
A veterinarian reads that 15% of dogs are allergic to chicken. However, he claims that the actual proportion is less than this. He randomly selects 15 of his customers and asks them if their dog is allergic to chicken. 3 of them say yes. Assume the population is normally distributed and use a=0.01. Suppose the test statistic is -1.11 Which function in excel finds the p=value?
=NORM.DIST(-1.11,0,1,TRUE)
A sociologist wishes to test H0: µ =42 vs. Ha: µ<42. The sociologist takes a sample of size 100 and calculates a standardized test statistic of -2.34. To calculate a p-value for the test in Excel, the sociologist should use:
=NORM.DIST(-2.34,0,1,TRUE)
A nutritionist claims that the average amount of sugar in a 16oz soda is at least 50 g. He randomly samples 10 sodas and finds they contain an average of 54g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use a=0.10 to test the claim. Suppose the test statistic is -1.22 Which function in Excel finds the p-value?
=T.DIST(-1.22,9,TRUE)
What must be done before an interpretation about a hypothesis test can be provided?
A decision about H0 must be made
A test is made of H0: µ = 20 versus Ha: µ ≠ 20. Suppose the true value of µ is 25, and H0 is rejected. Determine whether the outcomes is a Type I error, a Type II error, or a correct decision
Correct Decision
which of the following symbols denotes a hypothesis that includes an equality
H0
A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use a = 0.05 to test the claim. State the hypotheses
H0: µ ≤ 300 Ha: µ > 300 (claim)
A nutritionist claims that the average amount of sugar in a 16oz soda is at least 50 g. He randomly samples 10 sodas and finds they contain an average of 54g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use a=0.10 to test the claim. What are the hypotheses?
H0: µ ≥ 50 claim Ha: µ < 50
A diabetic claims that the average cost of insulin per year for a type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5,800 with a standard deviation of $575. Use a=0.05 to test the claim.
H0: µ=5705 (claim) Ha: µ≠5705
Which statement are true in hypotheses testing?
If we reject H0 when H0 is in fact true, we made Type I error One will reject H0 if the p-value is smaller than the significance level
The null hypothesis for a problem is that the population proportion is at least 0.22 Which type of test will be used?
Left-tailed test
The null hypothesis for a problem is that the population proportion is at least 0.22. Which type of test will be used?
Left-tailed test
Which of the following comes after finding the p-value in the p-value method?
Making a decision about H0
A researcher uses a =0.10 and finds a p-value -0.01 What should their decision be?
Reject H0
A veterinarian reads that 15% of dogs are allergic to chicken. However, he claims that the actual proportion is less than this. He randomly selects 15 of his customers and asks them if their dog is allergic to chicken. 3 of them say yes. Assume the population is normally distributed and use 𝛼=0.01α=0.01. Suppose the p-value is 0.002. What is the decision?
Reject H0
An English professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds the average amount of semicolons is 8.5. Assume the population is normally distributed and use 𝛼=0.05α=0.05to test the claim. Suppose the p-value is 0.003. What is the decision?
Reject H0
An english professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds that the average amount of semicolons is 8.5. Assume the population is normally distributed and use a=0.05 to test the claim. Suppose the p-value is 0.003. What is the decision?
Reject H0
Let p be the proportion of all adults who are in favor of outlawing cigarettes. A researcher testing the hypotheses: 𝐻0:𝑝=0.23;𝐻𝑎:𝑝≠0.23H0:p=0.23;Ha:p≠0.23 calculates a p-value of 0.00003. The researcher will likely
Reject the null hypothesis
Let μ be the average yield of a genetically modified tomato plant. A farmer tests the following hypotheses: H0:𝜇 =20; Ha: μ >20, and calculates a p-value of 0.00007. The farmer will likely
Reject the null hypothesis
What is the first step of the p-value method?
Stating the hypotheses
A certain type of fiber optic cable transmits light a mean distance of 58 km. A research team wishes to invertigate if a modiciatiion in the manufacturing process will increase the mean acceptable transmission distance. A sample of 20 batches of cable is prodiced under the new process are tested. The sample is 60.3km with sample standard deviation of 2.31km. Assukme the population is normally distributed. To test H0: µ =58 verses Ha: µ > 58, the team should use a:
T-test
Which of the following statements would correspond to an alternative hypothesis?
The population mean is not 21
A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5, 912 with a standard deviation of $300. Use 𝛼=0.05α=0.05to test the claim. If the decision is to reject 𝐻0H0, what should the interpretation be?
There is enough evidence to reject the claim
If the claim is that the population mean is equal to 8,000,000 and the decision is to reject H0, what should the interpretation be?
There is enough evidence to reject the claim
If the claim is that the population mean is less than to 0.46 and the decision is fail to reject H0, what should the interpretation be?
There is not enough evidence to support the claim
If the claim is that the population proportion is less than 0.46 and the decision is fail to reject 𝐻0H0, what should the interpretation be?
There is not enough evidence to support the claim
After correctly conducting a test of hypothesis, you have rejected the null hypothesis. The null hypothesis may still be true.
True
If H0: 𝜇 = 969, then the test will be _______
Two-Tailed
The alternative hypothesis for a probelm is that the population mean is not 42. Which type of test will be used?
Two-tailed test
Which symbol corresponds to the level of significance in a problem?
a
The null and alternative hypotheses are statement about:
a population parameter
A university administrator wishes to know if there is a difference in average starting salary for graduates with master's degrees in engineering and those with master's degrees in business. The average starting salary for graduates with master's degrees in engineering $83,000. The administrator samples 42 former students with master's degrees in business and finds an average starting salary of $61,000. The administrator tests the following hypotheses: 𝐻0:𝜇=83000;𝐻𝑎:𝜇<83000H0:μ=83000;Ha:μ<83000. In this scenario, the appropriate test statistic is:
b
A university administrator wishes to know if there is a difference in average starting salary for graduates with master's degrees in engineering and those with master's degrees in business. The average starting salary for graduates with master's degrees in engineering $83,000. The administrator samples 42 former students with master's degrees in business and finds an average starting salary of $61,000. The administrator tests the following hypotheses: H0: 𝜇= 83000; Ha:𝜇 <83000 In this scenario, the appropriate test statistic is:
b, z= x-
A diabetic claims that the average cost of insulin per year for a type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5,800 with a standard deviation of $575. Use a=0.05 to test the claim. Suppose the p-value is 0.0856 What is the decision?
fail to reject
A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5, 800 with a standard deviation of $575. Use α=0.05 to test the claim. Suppose the p-value is 0.0856. What is the decision?
fail to reject H0
A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use α=0.05 to test the claim. Suppose the p-value is 0.99.
fail to reject H0
A forensic anthropologist claims that 80% of female skeletons have a sub-pubic angle less than the often-cited 90 degrees. She randomly selects 200 skeletons and finds that 150 have an angle less than 90 degrees. Use α=0.10to test the claim. Suppose the p-value is 0.25. What is the decision?
fail to reject H0
A researcher uses a= 0.05 and finds a p-value = 0.10. What should their decision be?
fail to reject Ho
Let p be the proportion of all adults who are in favor of outlawing cigarettes. A researcher testing the hypotheses: H0: p=0.23; Ha: p ≠ 0.23 calculates a p-value of 0.489. The researcher will likely
fail to reject the null hypothesis
Let µ be the average yield of a genetically modified tomato plant. A farmer tests the following hypotheses. H0: µ = 20; Ha: µ > 20, and calculates a p-value of 0.459. The farmer will likely
fail to reject the null hypothesis
After finding the test statistic, what is the next step in the p-value method?
finding the p-value
If H0: p ≥ 0.80, then Ha:
p < 0.80
A nutritionist claims that the average amount of sugar in a 16 oz soda is at least 50 g. He randomly samples 10 sodas and finds they contain an average of 54 g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use α=0.10to test the claim. Suppose the p-value is 0.0854.
reject H0
A nutritionist claims that the average amount of sugar in a 16 oz soda is at least 50 g. He randomly samples 10 sodas and finds they contain an average of 54 g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use 𝛼=0.10α=0.10to test the claim. Suppose the p-value is 0.0854. What is the decision?
reject H0
A researcher wishes to test the following hypotheses: H0: p=0.23; Ha: p ≠ 0.23. The reasearcher takes a sample and performs a test which yields a p-value of 0.03. At a significance level of 5%, the researcher should ________ the null hypothesis. There _______ sufficient evidence to claim that the proportion differs from 23%
reject; is
An industry association asserts that the average age of all self-described fly fishermen is 42.8 years. A sociologist suspects that it is higher. The sociologists tests 𝐻0:𝜇=42.8; 𝐻𝑎:𝜇>42.8H0:μ=42.8; Ha:μ>42.8, and calculates a p-value of 0.003. At a significance level of 5%, the sociologist should ________ the null hypothesis. There ________ sufficient evidence to claim that the average age is higher than 42.8.
reject; is
A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use a = 0.05 to test the claim. Which distribution should be used to test the claim?
t-distribution
A fashion company releases a new line of prom dresses that are all under $100. They claim this is a bargain because the average cost of a prom dress is over $300. A customer decides to test this, and takes a random sample of 25 dresses. She finds the mean is $250 with a standard deviation of $10. Assume the population is normally distributed and use 𝛼=0.05α=0.05 to test the claim. Which distribution should be used to test the claim?
t-distribution
A nutritionist claims that the average amount of sugar in a 16 oz soda is at least 50 g. He randomly samples 10 sodas and finds they contain an average of 54 g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use 𝛼=0.10α=0.10to test the claim. Which distribution should be used?
t-distribution
A nutritionist claims that the average amount of sugar in a 16oz soda is at least 50 g. He randomly samples 10 sodas and finds they contain an average of 54g of sugar with a standard deviation of 3 g. Assume the population is normally distributed and use a=0.10 to test the claim. Which distribution should be used?
t-distribution
Let µ be the average starting salary for graduates with a master's degree in business. A university administrator test the following hypotheses: H0: µ=83000; Ha: µ < 83000, and calculates a p-value of 0.004. At the 5% level of significance, the administrator should conclude that:
the average starting salary is less than $83000
The level of significance is ______
the maximum allowable probability of rejecting the null hypothesis when its true
The p-value is
the probability of obtaining a value as extreme or more extreme than the observed value by chance alone, assuming the null hypothesis is true
An english professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds that the average amount of semicolons is 8.5. Assume the population is normally distributed and use a=0.05 to test the claim. Suppose the decision is to fail to reject H0. Then the interpretation would be:
there is not enough evidence to support the claim
if a > p-value, we reject H0
true
If H0: μ =969, then the test will be _____________.
two-tailed
A diabetic claims that the average cost of insulin per year for a Type 1 diabetic is $5,705. She takes a sample of 100 Type 1 diabetics and finds their average cost is $5, 800 with a standard deviation of $575. Use 𝛼=0.05α=0.05to test the claim. Which distribution should be used?
z-distribution
A forensic anthropologist claims that 80% of female skeletons have a sub-pubic angle less than the often-cited 90 degrees. She randomly selects 200 skeletons and finds that 150 have an angle less than 90 degrees. Use a= 0.10 to test the claim. Which distribution should be used?
z-distribution
A veterinarian reads that 15% of dogs are allergic to chicken. However, he claims that the actual proportion is less than this. He randomly selects 15 of his customers and asks them if their dog is allergic to chicken. 3 of them say yes. Assume the population is normally distributed and use a=0.01. Which distribution should be used?
z-distribution
An english professor is studying the use of semicolons over time. She estimates that in the Georgian era, authors used more than 8 semicolons per page. It is well known in her field that the standard deviation of semicolons in this era is 2. She randomly selects 25 pages from different books and finds that the average amount of semicolons is 8.5. Assume the population is normally distributed and use a=0.05 to test the claim. Which distribution should be used?
z-distribution
A standard painkiller is known to bring relief in 3.5 minutes on average (μ). A new painkiller is hypothesized to bring faster relief to patients. A sample of 40 patients are given the new painkillers. The sample yields a mean of 2.8 minutes and a standard deviation of 1.1 minutes. To test H0: μ =3.5 vs. Ha: μ <3.5, the researchers should use a
z-test
A medical laboratory claims that 85% of all COVID-19 tests that it performs yield results in 2 days or less. A government agency randomly samples 150 such tests, and finds that 82% of the sampled tests gave results in 2 days or less. The agency wishes to test the following hypotheses: H0: p =0.85; Ha: p <0.85. In this scenario, the appropriate test statistic is:
z= 𝑝̂-p0 (and more)
if Ha: µ > 0.85, then H0:
µ ≤ 0.85
In a random sample of 200 adults, 54 say they are in favor of outlawing cigarettes. Let p be the proportion of all adults who are in favor of outlawing cigarettes. A researcher wishes to test the following hypotheses: H0: p=0.23; Ha: p≠0.23.
𝑝̂ = 0.27 and p0=0.23
