Week 4 Part A: Confidence Intervals, Reviews, Exam #2
A random sample of 100 visitors to a popular theme park spent an average of $142 on the trip with a standard deviation of $47.5. Which of the following would the 98% confidence interval for the mean money spent by all visitors to this theme park?
($130.77, $153.23)
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 randomly selected members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. Find the 90% confidence interval.
(2.166, 2.634) StatCrunch > Stat > T Stats > One Sample > With Summary > Enter data as specified and calculate
The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week that is generated in city. The study included 120 residents whose mean number of pounds of trash generated per person per week was 31.5 pounds and the standard deviation was 7.8 pounds. What is the confidence interval for the mean number of lbs of trash per person per week that is generated in the city?
(30.090, 32.910) StatCrunch > Stat > T Stats > One Sample > With Summary > Enter data as specified and calculate
A biologist has taken a random sample of a specific type of fish from a large lake. A 95 percent confidence interval was calculated to be 6.8 ± 1.2 pounds. Which of the following is true?
In repeated sampling, 95% of the time the true population mean of fish weight will be captured in the constructed interval.
When did this appear on the news according to the video?
March 18, 2020
In a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football. Construct a 95% confidence interval for the proportion of adults in the United States who say that their favorite sport to watch is football. Construct a 95% confidence interval and interpret its meaning using PANIC. P--> mu = 𝜇=μ=The true proportion of all US adults who watch football as their favorite sport. A--> Random stated in problem. 354 (number of successes) > 10 N--> One proportion Z confidence interval I--> (0.265 , 0.316) C--> We are 95% confident that between 26.5% and 31.6% of all US adults prefer to watch football as their favorite sport. Which of the PANIC steps are wrong / incomplete? Select all that apply
P, A
A Gallup poll conducted a random sample survey in 2005 asked 1006 Americans how many books did they read in the past year. Results of the survey indicated the mean to be 13.4 books, with a sample standard deviation of 16.6 books. Construct a 99% confidence interval and interpret its meaning. P--> mu = the true mean number of books read by 1006 Americans from 2004 - 2005 A--> random stated, n = 1006 > 30, all assumptions met N--> T Interval, or 1 samp t int I--> (11.05, 14.98) C--> we are 99% confident that the true mean number of books read by 1006 Americans from 2004 - 2005 is between 11.05 to 14.98 books.
P, I, C
Suppose a simple random sample of 150 students is drawn from a population of 3000 college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the point estimate?
Point Estimate = (Upper Confidence Limit) + (Lower Confidence Limit) / 2 StatCrunch > Stat > T Stats > One Sample > With Summary > Enter data as specified and calculate UL = 116.61341 LL = 113.38659 116.6134 + 113. 3866 = 230 230 /2 = 115
Is the picture being discussed in the video focused on proportions or means?
Proportions
A quality control specialist at a plate glass factory must estimate the mean clarity rating of a new batch of glass sheets being produced using a sample of 18 sheets of glass. The actual distribution of this batch is unknown, but preliminary investigations show that a normal approximation is reasonable. The specialist decides to use a t-distribution rather than a z-distribution because
The variability/SD of the population is unknown.
To create a sampling distribution, take lots of random samples, calculate all their sample means or sample percentages and then make a graph of all the sample means or sample percentages.
True
We can approximate the standard error from a sampling distribution without a formula
True
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 randomly selected members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. Were the A --> Assumptions met
Yes
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. Round your answers to two decimal places. The sampling distribution follows what kind of distribution?
t - distribution
A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. What is the correct Parameter?
𝜇μ = the true mean number of days per week that Americans who are members of a fitness club go to their fitness center
What is the LL lower limit of the confidence interval found for the study being cited in the video? Write your answer as a decimal, not as a percentage.
0.152
What is the UL upper limit of the confidence interval found for the study being cited in the video? Write your answer as a decimal, not as a percentage.
0.248
What is the point estimate for the study being shown?
20%
150 accidents that required treatment in an emergency room were randomly sampled from hospitals across the country. 36% involved children less than 6 years of age. Find the 90% confidence interval to estimate the true proportion of all accidents requiring ER treatment that involve a child less than 6 years old. P-> p = The true proportion of all accidents requiring ER treatment that involve a child less than 6 years old . A-> Random? Yes, stated the sample was random. np ̂ = (150)(0.36) = 54 ≥ 10 ; nq ̂ = (150)(0.64) = 96 ≥ 10 N-> 1 proportion-z confidence interval I-> (0.2955 , 0.4245) C-> We are 90% confident that the true proportion of all accidents requiring ER treatment that involve a child less than 6 years old is between 0.2955 and 0.4245. Which of the PANIC steps are wrong / incomplete? Select all that apply
All are correct
A research and development engineer is preparing a report for the board of directors on the battery life of a new cell phone they have produced. At a 95% confidence level, he has found that the battery life is 3.2 ± 1.0 days. He wants to adjust his findings so the margin of error is as small as possible. Which of the following will produce the smallest margin of error?
Decrease the confidence level to 90%.
Calculating standard error is not important in statistics, we only need to look at the regular standard deviation of a single data set.
False
If it's a random sample, it will always give the same sample values.
False
The standard error of a sampling distribution is higher than the standard deviation of a single data set.
False
