stats ch 9
We are 95% confident that the mean number of hours worked by adults in this country in the previous week was between 41.641.6 hours and 44.944.9 hours.
correct
Determine if the following statement is true or false. A confidence interval indicates how confident we are with the hypothesized value for the population mean.
false
level of confidence c
is the middle c% of the standard normal distribution.
Compute the critical value 2zα/2 that corresponds to a 91% level of confidence.
level of confidence =(1-a)*100% .85=(1-a)*1 1-.85=.15 .15/2=.075 z score= -1.44
Days before a presidential election, an article based on a nationwide random sample of registered voters reported the following statistic, "52% (plus or minus±3%) of registered voters will vote for Robert Smith." What is the "plus or minus±3%" called?
margin of error
critical value zα/2
the z-score taken at the one end
Determine the point estimate of the population mean and margin of error for the confidence interval. Lower bound is 17, upper bound is 29.
-The point estimate of the population mean is 1) upper+lower/2 29+17/2=23 -The margin of error for the confidence interval is 1)upper-lower/2 29-17/2=6
Find the critical t-value that corresponds to 96% confidence. Assume 18 degrees of freedom.
1) 1-.96=.04 2) .04/2=.02
Which of the following is a correct explanation of what a confidence interval is?
A confidence interval is a range of values used to estimate the true value of a population parameter. The confidence level is the probability the interval actually contains the population parameter, assuming that the estimation process is repeated a large number of times.
How does the decrease in confidence affect the sample size required?
Decreasing the confidence level decreases the sample size needed. Increasing the level of confidence increases the sample size required. For a fixed margin of error, greater confidence can be achieved with a larger sample size.
A graduate student wanted to estimate the average time spent studying among graduate students at her school. She randomly sampled graduate students from her school and obtained a 99% confidence interval of (17,25) hours/week. Which of the following would be true if the level of confidence was lowered to 95%?
The width of the confidence interval would be smaller.
A research organization wanted to estimate the average number of hours a college student sleeps per night during the school year. After randomly sampling 150 college students, the research organization determined the following 95% confidence interval: (7.1 hours/night, 7.5 hours/night). What would happen to the width of the confidence interval if the level of confidence increased (assuming everything else remained the same)?
The width of the confidence interval would increase.
A graduate student wanted to estimate the average time spent studying among graduate students at her school. She randomly sampled graduate students from her school and obtained a 99% confidence interval of (17.3,22.5) hours/week. In the context of the problem, which of the following interpretations is correct?
We are 99% sure that the average amount of time spent studying among graduate students at this student's school is between 17.3 and 22.5 hours per week.
formulas for n
always round up
A confidence interval for a population mean __________.
A confidence interval for a population mean gives possible values the true population mean will be with a certain level of confidence.
Find the t-value such that the area in the right tail is 0.01 with 9 degrees of freedom.
1) if to the right chart find .01 and 9 2) if to the left put - in front
Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided. Lower bound=0.086, upper bound=0.314, n=1000
1- (point estimate)upper bound+lower bound/2 2-(margin error)upper bound-lower bound/2 3- (# of individuals)n value * answer for 1
Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error, E?
As the level of confidence increasesincreases, the size of the interval increasesincreases.
How does increasingincreasing the sample size affect the margin of error, E?
As the sample size increasesincreases, the margin of error decreasesdecreases.
What effect does doubling the required accuracy have on the sample size?
Doubling the required accuracy nearly quadruples the sample size.
We are 95% confident that the mean number of hours worked by adults in a particular area of this country in the previous week was between 41.641.6 hours and 44.944.9 hours.
Flawed. The interpretation should be about the mean number of hours worked by adults in the whole country, not about adults in the particular area.
There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 41.641.6 hours and 44.944.9 hours.
Flawed. This interpretation implies that the population mean varies rather than the interval.
95% of adults in this country worked between 41.641.6 hours and 44.944.9 hours last week.
Flawed. This interpretation makes an implication about individuals rather than the mean.
Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true?
For a fixed margin of error, smaller samples will mean lower confidence. For a certain confidence level, you can get a smaller margin of error by selecting a bigger sample. For a given confidence level, a sample 9 times as large will make a margin of error one third as big. For a given sample size, reducing the margin of error will mean lower confidence.
Which of the following would increase the width of a confidence interval for a population mean?
Increase the level of confidence
In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5. Provide two recommendations for decreasing the margin of error of the interval.
Increase the sample size. Decrease the confidence level.
Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
No, the population needs to be normally distributed.
A trade magazine routinely checks the drive-through service times of fast-food restaurants. Upper AA 9595% confidence interval that results from examining 773773 customers in onefast-food chain's drive-through has a lower bound of 159.7159.7 seconds and an upper bound of 162.7162.7 seconds. What does this mean?
One can be 9595% confident that the mean drive-through service time of this fast-food chain is between 159.7159.7 seconds and 162.7162.7 seconds.
Use the confidence interval to find the margin of error and the sample mean.(1.63,2.01)
The margin of error= 2.01-1.63/2= .19 The sample mean is= 2.01+1.63/2=1.82
construct a 95% confidence interval of the population proportion using the given information.
x=175 n=250 175/250=.7 1-.95=.05 .05/2=.025 z score of .025=-1.9599 =positive 1.9599 upper= sqrt of (p hat (1-p hat)) /n =sqrt of (.7 (1-.7)) /250 =.028982 .028982 * za/2 =.028982 *.025=
