11.1 & 11.2
Identify the sample in the given scenario:
"Of the 1689 people in the U.S. surveyed by Fit and Healthy magazine, 826 reported being self-conscious about their weight."
A) 1689 people surveyed
B) U.S. population
C) 826
D) None given
A) 1689 people surveyed
Find the mean of the data from the "Building Toy Pieces" data set.
204.25
Calculate the standard score of the given 𝑥-value, 𝑥=63.2, where 𝑥̅ = 68.3, 𝑠 = 6.2. Round your answer to two decimal places.
-0.82
Can we say with 80% certainty that city G had at least 600 cases of this virus among adults last month?
A) No. Because the sample mean for city G does not equal 600, we cannot conclude with 80% confidence that city G had at least 600 cases of this virus among adults last month.
B) Yes. Because the sample mean is above 600, we can be 80% confident that city G had at least 600 cases of this virus among adults last month.
C) No. Although the sample mean for city G falls above 600, the confidence interval still contains 600. Therefore, we cannot conclude with 80% confidence that city G had at least 600 cases of this virus among adults last month.
D) Yes. Because the entire confidence interval is above 600, we can be 80% confident that city G had at least 600 cases of this virus among adults last month.
C) No. Although the sample mean for city G falls above 600, the confidence interval still contains 600. Therefore, we cannot conclude with 80% confidence that city G had at least 600 cases of this virus among adults last month.
Using the x and y data set: Calculate the correlation coefficient for the data. Round your answer to the nearest thousandth.
r=0.912
Determine if the numerical value describes a population parameter or a sample statistic.
"66% of all students at the local university voted in the last election."
Population parameter
Find the standard deviation of the sample data set "Building Toy Pieces"
109.05
The rainfall in a town last year measured 28 inches. If the annual rainfall has a mean of 47.73 inches and a standard deviation of 8.58 inches, determine the 𝑧-score of last year's rainfall. Round your answer to two decimal places.
-2.30
A recent survey of 800 American adults found that 624 preferred cereal A over cereal B.
Step 1. Use the best point estimate to estimate the percentage of all American adults who prefer cereal A over cereal B.
78%
30Use the x and y data table: Given that the linear relationship between 𝑥 and 𝑦 is statistically significant, find the linear regression line in the form 𝑦^=𝑎𝑥+𝑏 for this relationship. Round 𝑎 and 𝑏 to the nearest thousandth.
y^=2.934x+34.446
The boxplot shows the score from the final exam in an English 101 course. What was the median score?
70
Find the median of the data set "Building Toy Pieces"
196.5
You want to know the percentage of medical equipment companies that earned revenue less than 79 million dollars. If the mean revenue was 60 million dollars and the data has a standard deviation of 11 million, find the percentage. Assume that the distribution is normal. Round your answer to the nearest hundredth.
95.82%
A recent survey of 800 American adults found that 624 preferred cereal A over cereal B.
Step 2. Use the general rule for approximating margin of error for polls to compute the margin of error for a 95% confidence interval for this survey. Round your answer to one decimal place (i.e. 15.1%)
3.5%
Find the critical value to the nearest thousandth when r = 0.735 α=0.05 n=7
0.754
Identify the sampling technique used in the given scenario:
A soda bottling company will randomly test 10 bottles from each of its 20 machines to assure the product meets quality standards.
A) Random
B) Stratified
C) Convenience
D) Cluster
E) Systematic
B) Stratified
Calculate the five-number summary of the given data.
16, 14, 2, 10, 20, 23, 4, 13, 17, 7, 17, 5, 25, 22
2, 7, 15, 20, 25
What percentage of the area under the normal curve is between the following 𝑧-scores? Round your answer to two decimal places.
z1=-2.46, z2=-1.35
8.16%
A recent survey of 800 American adults found that 624 preferred cereal A over cereal B.
Step 3. Use the margin of error you computed together with the point estimate to create a 95% confidence interval for this survey. Write your answer as an interval: i.e. (12.3%,15.4%)
(74.5%, 81.5%)
Using the critical value of 0.754 and an r value of 0.735, is the correlation coefficient statistically significant?
a) Yes, the linear relationship between the variables is statistically significant at the 0.05 level of significance, because |r|>critical value.
b) Yes, the linear relationship between the variables is statistically significant at the 0.05 level of significance, because |r|>0.
c) Yes, the linear relationship between the variables is statistically significant at the 0.05 level of significance, because |r| < critical value.
d) No, the linear relationship between the variables is not statistically significant at the 0.05 level of significance, because |r|<critical value.
e) No, the linear relationship between the variables is not statistically significant at the 0.05 level of significance, because |r|<0
f) No, the linear relationship between the variables is not statistically significant at the 0.05 level of significance, because |r| > critical value.
d) No, the linear relationship between the variables is not statistically significant at the 0.05 level of significance, because |r|<critical value.
Identify the sampling technique used in the given scenario:
An advertising agency wants to analyze the ages of typical moviegoers in a suburban area. There are three theaters in the area, all of which show the same films and have a similar customer base. The agency decides to survey all of the customers at one of the three locations.
A) Convenience
B) Systematic
C) Cluster
D) Stratified
E) Random
C) Cluster
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.53 and a standard deviation of 0.43. Using the empirical rule, what percentage of the students have grade point averages that are between 2.1 and 2.96?
68%
Suppose that IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. Using the empirical rule, what percentage of IQ scores are greater than 85? Please do not round your answer.
84%
Step 4. Suppose that the survey had resulted in the following:
Point Estimate: 82% Confidence Interval: (78.2%, 85.8%)
Which of the following is the best interpretation of the point estimate 82% and confidence interval (78.2%, 85.8%)?
A) We are 95% confident that 82% of all American adults prefer cereal A over cereal B.
B) We are 95% confident that the true percentage of the 800 respondents who prefer cereal A over cereal B is between 78.2%and 85.8%.
C) We are 95% confident that 82% of the 800 respondents prefer cereal A over cereal B.
D) We are 95% confident that the true percentage of American adults who prefer cereal A over cereal B is between 78.2% and 85.8%.
D) We are 95% confident that the true percentage of American adults who prefer cereal A over cereal B is between 78.2% and 85.8%
The average temperature in a certain city has a statistically significant correlation to the monthly precipitation, measured inches. The regression line 𝑦^=0.15𝑥+13.14 models this relationship when the temperature is between 75 and 90 degrees. Use the line to predict the monthly precipitation if the temperature is 83 degrees. Round your answer to the nearest hundredth.
25.59 inches