Probability
The probability of event A is 0.35. The probability of event B is 0.45. If events A and B are independent, then:
A. P(A or B)= 0.8 B. P(A and B)= 0
C. P(A or B)= 0.6425. D. P(A or B)= 0.1575
C. P(A or B)= 0.6425
Below are summary statistics for the number of steps walked per day for a sample of adults
Min: 850 Q1: 3100 Median: 6700 Q3: 11900 max: 14200 mean: 7900
Which of the following is correct?
A. the data is left skewed
B. the data is right skewed
C. the data is symmetric
D. we cannot tell the shape of the distribution without a graph
B
In one study students in a class responded to a questionnaire asking about their television usage and their class grades. In a second study half of a class were instructed to watch exactly one hour of television per day, the other half were told to watch five hours per day, and then their class grades were compared. Were these observational studies or experiments?
The first was an observational study while the second was an experiment
A researcher wishes to estimate the population proportion of U.S. adults who have made at least one trip to the emergency room within the last year. They wish to estimate the proportion to within 2% with 90% confidence. How many individuals should be included in the sample?
1692
A survey was conducted to estimate the proportion of adults who view teaching as a prestigious profession. A 95% confidence interval was calculated to be (0.459,0.521). What is the point estimate and merging of error?
Point estimate: 0.49
ME: 0.031
In a certain region the mean home price was $425,000 with a standard deviation of $51,000. Which is more unusual, a house that costs $305,000 or a house that costs $510,000? Why?
The $305,000 house, since the z-score was farther from zero.
Does the age at which a child begins to talk predict future results on an aptitude test? A study was done with age at first word as the explanatory variable and aptitude test score as the response variable. The regression equation was calculated as y^= 109.8738-1.1270x with r= -0.8
What percentage of the variation in test score can be explained by age at first word?
64%
A researcher selects twenty-five students at random from each grade level at a high school and asks them to fill out a survey about study habits. This is an example of:
A. simple random sample
B. stratified random sample
C. Cluster sample
D. systematic sample
B. Stratified random sample
A politician is trying to decide whether to vote for a new tax bill that calls for substantial reforms. He will only vote for the bill if he believes that more than 50% of voters in his district support the bill. A random sample of voters in his district is used to test the following hypotheses: Ho: p= 0.5 vs. Ha: p>0.5 Which of the following describes a type II error?
A. The politician believes more than 50% of voters in his district support the bill so he votes for it, but the bill is not supported by majority of voters
B. The politician believes more than 50% of voters support the bill so he cotes for it, and the bill is supported by majority of voters
C. The politician does not believe more than 50% of voters support the bill so he votes against it, and the bill is not supported by majority of voters
D. The politician does not believe more than 50% of voters support the bill so he votes against it, and the bill is supported by the majority of voters
D.
Assume men's weights follow a normal distribute with a mean of 189 pounds and standard deviation of 30 pounds. Use the empirical rule to estimate the percentage of women who weigh between 159 and 249 pounds?
81.5%
Assume we know that the probability that an adult is underemployed is 0.35. Four adults are selected at random (therefore we can assume independence). What is the probability that at least one of the adults is underemployed?
0.8215
y^= -31.6+ 0.012x correlation= 0.639
A customer has an income of $48,000 and a yearly purchases of $510. What is the residual for this customer?
-34.4
Flat screen TVs require high-quality glass with very few flaws. A television manufacturer inspected the glass panels received from its supplier. It was found that 48% of panels had no flaws, 27% of panels had one flaw, 16% had two flaws and 9% had three flaws. Calculate the standard deviation of the number of flaws in a glass panel received from this supplier.
0.99
A manufacturer of car batteries claims that his product is used in at least 20% of all cars. A sample of 150 cars is used to test whether the product is used in less than 20% of all cars. The test statistic is calculated to be -1.79. Using a 5% level of significance, the conclusion would be
A. There is sufficient evidence to show the manufacturer's claim is correct
B. There is insufficient evidence to show the manufacturer's claim is incorrect
C. There is sufficient evidence to show the manufacturer's claim is incorrect
D. There is insufficient evidence to show the manufacturer's claim is incorrect
C.
"On hold" times for callers to a local insurance company are known to be normally distributed, with a standard deviation of 1.4 minutes. What is the mean caller "on hold" time if only 9.5% of callers wait for more than 6 minutes.
4.166
In a group of 16 college students, there are 7 who are graduate students. If we select two college students at random from the group (without replacement), what is the probability we select exactly one who is a graduate student?
0.5250
A student wanted to examine the relationship between the average daily protein intake and LDL cholesterol levels. He randomly selected 10 patients who were willing to participate in his research. The correlation was calculated to be -0.81. What can we conclude?
A. Increased protein intake causes higher LDL cholesterol levels
B. Increased protein intake causes lower LDL cholesterol levels
C. Increased protein intake is associated with higher LDL cholesterol levels
D. Increased protein intake is associated with lower LDL cholesterol levels
D
What are two ways to decrease the margin of error of a confidence interval?
decrease the confidence level
increase the sample size
Suppose 25% of American adults meet the surgeon general's recommendation for daily physical activity. If a random sample of 250 American adults is taken, what are the mean and standard deviation of the proportion that meet the recommendation? What is the probability that no more than 31% of the sample of 250 adults meet the recommendation?
mean: 0.25
sd: 0.0274
probability: 0.9857
The average phone bill for families in California is $110. You take a random sample of 30 families and get an average price of $115.50 with a sample standard deviation of $10. Is there sufficient evidence to show that the average phone bill exceeds $110?
reject Ho
It is known that 36% of young adults have more than one job. If we randomly select 11 young adults, what is the probability that fewer than 3 of the 11 have more than one job?
0.1814
According to the state department, only twenty seven percent of Americans carry a valid passport. Suppose we take a random sample of 11 Americans. Which of the following best describes the distribution of x=number of Americans that carry a valid passport?
X ~ B (11, 0.27)
T/F
If we fail to reject a null hypothesis at level of significance alpha, then the hypothesis test is statistically significant at level alpha
false
A survey was conducted to determine the proportion of adults who are the economy as good. Based on the responses of a random sample of adults a 96% confidence interval was calculated to be (0.198, 0.251). Use the confidence interval to test the claim that 20% of adults rate the economy as good.
A. since 0.20 does not fall in the confidence interval, we have enough evidence to reject the claim
B. since 0.20 falls in the confidence interval, we have enough evidence to prove that the claim is true
C. since 0.20 does not fall in the confidence interval, we do not have enough evidence to reject the claim
D. Since 0.20 falls in the confidence interval, we do not have enough evidence to reject the claim
D
A company that makes candy bars states that there are 200 calories per bar. Suppose you wish to verify this claim. During your tests, you find that a random sample of 35 bars has a mean of 195 calories with a standard deviation of 5.5. At the 0.01 level of significance, can you reject the companies claim?
fail to reject