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Mary likes M&M's. The M&M website claims that 10% of the M&M's in a bag are blue. Mary believes that the color blue may actually occur more frequently. She buys a bag from a vending machine and finds that 13% of the M&M's in the bag are blue. Does the data support her claim? Which are the correct statements for the null and alternative hypotheses? A) B) C) D)
Points Earned: 3.0/3.
Correct
Answer(s):
A
Ho: μ = 100 & Ha: μ ≠ 100 Which scenario would lead to the smallest p-value? A) n=50 & sample mean is 80 B) n=50 & sample mean is 90 C) n=100 & sample mean is 110 D) n=100 & sample mean is 120
Points Earned: 3.0/3.
Correct
Answer(s):
D
Consider a disease where: the success rate for the standard treatment is .30. Evidence suggests a new treatment may have a higher success rate. The results from a study, where n = 100, found 35 were successfully treated with the new method. Which are the correct hypotheses?
A) Ho: p = .35 & Ha: p <. B) Ho: p = .35 & Ha: p >. C) Ho: p = .30 & Ha: p <. D) Ho: p = .30 & Ha: p >. Feedback: Hypotheses only include statements about population parameter values
Points Earned: 0.0/4.
Correct
Answer(s):
D
Consider a disease where: the success rate for the standard treatment is .30. Evidence suggests a new treatment may have a higher success rate. The results from a study, where n = 100, found 35 were successfully treated with the new method. Which describes the type 1 error for this problem? A) Claim new treatment success rate is higher than .30 when really it is not. B) Claim new treatment success rate is not higher than .30 when really it is.
Points Earned: 3.0/3.
Correct
Answer(s):
A
Consider a disease where: the success rate for the standard treatment is .30. Evidence suggests a new treatment may have a higher success rate. The results from a study, where n = 100, found 35 were successfully treated with the new method. Which distribution should be used to find the p-value?
A)
B)
C)
Points Earned: 3.0/3.
Correct
Answer(s):
A
When it is necessary to use the t table (t distribution): With _____ A) categorical data, when the population standard deviation is unknown B) categorical data, when the population proportion is unknown
C) quantitative data, when the population standard deviation is unknown D) quantitative data, when the population proportion is unknown Feedback: With quantitative day, proportions can never be a correct answer.
Points Earned: 0.0/3.
Correct
Answer(s):
C
Identify whether the question is asking for a confidence interval or a hypothesis test, along with the appropriate population parameter. Use each answer only once.
A. Confidence Interval:
proportion
B. Hypothesis Test:
proportion
C. Confidence Interval: mean
D. Hypothesis Test: mean
A nutritionist wants to determine if the average cholesterol level (mg/dl) for PSU students differs from 200 mg/dl. A random sample of 500 PSU students was obtained. A blood test to measure cholesterol level (mg/dl) was given to each selected student. A survey of Americans asks, “Do you believe that the country is moving in the wrong direction ("yes" or "no")?” The goal is to estimate the population proportion who say "yes"? How fast can a college student type on a computer? In a study, 20 selected students were asked to type a prepared article as fast as they could in a Word Document. The time in seconds was recorded for each student and used to estimate the average for all college students. Last year it was found that about 50% of students who attend college do not graduate within 6 years. There is evidence that for this year the percentage will be smaller than 50%?
Points
Earned:
Correct
Answer(s):
Hypothesis Test: mean:A nutritionist wants to determine if the
average cholesterol level (mg/dl) for PSU students differs from
200 mg/dl. A random sample of 500 PSU students was obtained.
A blood test to measure cholesterol level (mg/dl) was given to
each selected student., Confidence Interval: proportion:A survey
D A C B
How many of the 10 confidence intervals did not actually capture the true value of the population mean? A) 0 B) 3 C) 4 D) 7 E) 10 Feedback: Look for C.I's that do not contain 50
Points Earned: 3.0/3.
Correct
Answer(s):
B
Which is untrue about a population parameter? A population parameter ______ A) is a number that describes a population B) has a corresponding sampling distribution C) has a value that may or may not be known once the population is defined. D) can only assume one value once the population is defined Feedback: A sampling distibution suggests possible for the sample statistic
Points Earned: 3.0/3.
Correct
Answer(s):
B
A recent PSU survey found, by a 3% margin of error, 48% of PSU students participate in the newspaper readership program. The margin of error was calculated at 95% confidence. Suppose the margin of error was instead calculated at 98% confidence, which of the following would be true?
Statistically speaking, we can claim that a minority has been found: A) at 95% confidence but not at 98% confidence B) at 98% confidence but not at 95% confidence C) at both 95% confidence and 98% confidence D) at neither 95% confidence nor 98% confidence
Points Earned: 0.0/3.
Correct
Answer(s):
D
Which is untrue about the standard deviation? The standard deviation is _____ A) is an accurate measure of spread only when the data is normal in shape. B) roughly defined as the average distance of an observed value from the mean C) a sensitive measure of spread D) measures the amount of variation in the middle 50% of the data Feedback: Standard deviation requires a normal and can only be interpreted when considering the sample mean
Points Earned: 3.0/3.
Correct
Answer(s):
D
Suppose you obtain 100 samples and calculated 100 confidence intervals each at 90% confidence. How many of these intervals would you expect to capture the true value of the population parameter? A) 0 B) 9 C) 50 D) 90 E) 100
Points Earned: 3.0/3.
On a local highway the speed limit is listed as 60 mph. A random sample of 14 cars who traveled this road were obtained. The speed was determined for each car. Below are the results. Test of mu = 60 vs not = 60 Variable N Mean StDev SE Mean 95% CI T P Speed 14 66.9 14.3 3.8 (58.60, 75.10) 1.79 0. In terms of notation, which of the following is correct when referring to the number 14. mph on the Minitab output? A) B) C) D) E)
Points Earned: 3.0/3.
Correct
Answer(s):
D
On a local highway the speed limit is listed as 60 mph. A random sample of 14 cars who traveled this road were obtained. The speed was determined for each car. Below are the results. Test of mu = 60 vs not = 60 Variable N Mean StDev SE Mean 95% CI T P Speed 14 66.9 14.3 3.8 (58.60,
75.10) 1.79 0. Which is the value of the degrees of freedom that would be used in this instance? A) 13 B) 14 C) 15 D) 16
Points Earned: 4.0/4.
Correct
Answer(s):
A
On a local highway the speed limit is listed as 60 mph. A random sample of 14 cars who traveled this road were obtained. The speed was determined for each car. Below are the results. Test of mu = 60 vs not = 60 Variable N Mean StDev SE Mean 95% CI T P Speed 14 66.9 14.3 3.8 (58.60, 75.10) 1.79 0. Which confidence interval substitutions could correctly provide the result found on the Minitab output? Consider all numbers Use reasoning. A) B) C) Feedback: the T on the output (T = 1.79) is not the multiplier it is the test statistic. You have a small sample size where n = 15, so the t multiplier will be greater than 2.0 (1.96)
A) sample median is 1.79 standard deviations above the population median B) sample mean is 1.79 standard deviations above the population mean C) sample proportion is 1.79 standard deviations above the population proportion
Points Earned: 3.0/3.
Correct
Answer(s):
B
On a local highway the speed limit is listed as 60 mph. A random sample of 14 cars who traveled this road were obtained. The speed was determined for each car. Below are the results. Test of mu = 60 vs not = 60 Variable N Mean StDev SE Mean 95% CI T P Speed 14 66.9 14.3 3.8 (58.60, 75.10) 1.79 0. Which would be the correct conclusion for this hypothesis test? A) Can claim that the population mean equals 60 B) Can claim that the population mean is different from 60 C) Can not claim the the population mean equals 60 D) Can not claim that the population mean is different from 60
Points Earned: 0.0/3.
Correct
Answer(s):
D
On al local highway the speed limit is listed as 60 mph. A random sample of 15 cars who traveled this road were obtained. The speed was determined for each car. Below are the results.
Test of mu = 60 vs not = 60 Variable N Mean StDev SE Mean 95% CI T P Speed 14 66.9 14.3 3.8 (58.60, 75.10) 1.79 0. When using the 95% confidence interval, statistically what can we conclude? That, on the average, for this local highway, people drive at a speed that is greater than : A) 50 mph. B) 60 mph. C) 70 mph. Feedback: All C. I. values are above 50 mph
Points Earned: 2.0/2.
Correct
Answer(s):
A
A study asked a group of Americans, who recently lost their job but subsequently got hired for a new job, two questions: What was your salary at your previous job and what is your salary at your current job? The goal is to determine how much, on the average, the salary differs when comparing the previous salary to the current salary. These two samples are: A) independent with a categorical response variable B) independent with a quantitative response variable C) dependent with a categorical response variable D) dependent with a quantitative response variable
Points Earned: 2.0/2.
Correct
Answer(s):
D
USAToday , Oct 5, 2010: Women weigh heart-healthy alcohol, breast cancer risk:
C) 20
D) 40
Feedback: (Sample Estimate) +/- (Multiplier)(Standard Error) Since the multiplier for a 0% confidence interval is "0", the sample estimate represents the 0% confidence interval because the margin of erroe is 0. In this case it is the sample mean.
Points Earned: 2.0/2.
Correct
Answer(s):
D
At a given n and level of confidence, for which value of sample proportion will the confidence interval be the smallest? Use reasoning. A) sample proportion =. B) sample proportion =. C) sample proportion =. Feedback: Most variation at sample proportion = .5 as shown on graph - so the one that is the furthest has the smallest deviation
Points Earned: 0.0/1.
Correct
Answer(s):
C
Below are the inferential results (in Minitab) from a sample of 30 cholesterol levels (mg/dl). The response variable is : cholesterol level (mg/dl). Test of mu = 200 vs < 200 95% Upper N Mean StDev SE Mean Bound T P 30 193.00 22.00 4.0 199.82 -1.74 0. Which choice correctly describes how the p-value was computed when using the t distribution? Use all provided information. At df = 29, the probability that _____ A) t is greater than -1.74. B) t is less than -1.74.
Points Earned: 0.0/3.
Correct
Answer(s):
D
Below are the inferential results (in Minitab) from a sample of 30 cholesterol levels (mg/dl). The response variable is : cholesterol level (mg/dl). Test of mu = 200 vs < 200 95% Upper N Mean StDev SE Mean Bound T P 30 193.00 22.00 4.0 199.82 -1.74 0. Based on the output, which quantity estimates the average difference between the sample mean and the population mean for a sampling distribution based on n = 30. A) 4 B) 22 C) 30 D) 193 Feedback: asking for standard error
Points Earned: 0.0/2.
Correct
Answer(s):
A
Below are the inferential results from a sample of 30 cholesterol levels (mg/dl). The response variable is : cholesterol level (mg/dl). Test of mu = 200 vs < 200 95% Upper N Mean StDev SE Mean Bound T P
30 193.00 22.00 4.0 199.82 -1.74 0. Which is the correct conclusion for this hypothesis test? A) Can not claim the population proportion < 200. B) Can not claim the population mean < 200. C) Can claim population proportion < 200. D) Can claim the population mean < 200.
Points Earned: 3.0/3.
Correct
Answer(s):
D
Below are the inferential results (in Minitab) for a sample of 30 cholesterol levels (mg/dl). The response variable is : cholesterol level (mg/dl). Test of mu = 200 vs < 200 95% Upper N Mean StDev SE Mean Bound T P 30 193.00 22.00 4.0 199.82 -1.74 0. After making a conclusion, which error is now possible? A) type 1 error B) type 2 error
Points Earned: 0.0/2.
Correct
Answer(s):
A
