Stats Ch 9 Sec 1
Explain what "90% confidence" means in a 90% confidence interval.
If 100 different confidence intervals are constructed, each based on a different sample of size n from the same population, then we expect 90 of the intervals to include the parameter and 10 to not include the parameter.
A group conducted a poll of 2075 likely voters just prior to an election. The results of the survey indicated that candidate A would receive 45% of the popular vote and candidate B would receive 44% of the popular vote. The margin of error was reported to be 2%. The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means.
Since it is within the margin of error for candidate A to receive 43% of the popular vote and for candidate B to receive 46%, or for candidate A to receive 47% of the popular vote and for candidate B to receive 42%, the poll cannot predict the winner.
Construct a 95% confidence interval of the population proportion using the given information. x=120, n=300
The lower bound is . 345 The upper bound is . 455
Why does the margin of error decrease as the sample size n increases?
The margin of error decreases as the sample size n increases because the difference between the statistic and the parameter decreases. This is a consequence of the Law of Large Numbers.
Why does the margin of error increase as the level of confidence increases?
The margin of error increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter, the larger the margin of error.
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 specifiedcharacteristic, x, for the sample size provided. Lower bound=0.561, upper bound=0.819, n=1000
The point estimate of the population proportion is . 69 The margin of error is . 129 The number of individuals in the sample with the specified characteristic is 690
By how many times does the sample size have to be increased to decrease the margin of error by a factor of 1/4?
The sample size must be increased by a factor of 16 to decrease the margin of error by a factor of 1/4.
A poll of 1567 adults in a certain country found that 23% identified themselves as the followers of some religion. The margin of error was 5 percentage points with 95% confidence. Which of the following represents a reasonable interpretation of the survey results?
There is 95% confidence that the proportion of adults in a certain country who identify themselves as the followers of some religion is between 18% and 28%.
Express the confidence interval 0.333<p<0.999 in the form p±E.
p ± E = .666 ± .333
Which of the following groups has terms that can be used interchangeably with the others?
percentage, probability, and proportion
A ________ ________ is the value of a statistic that estimates the value of a parameter.
point estimate
Which of the following is NOT needed to determine the minimum sample size required to estimate a population proportion?
standard deviation
Compute the critical value zα/2 that corresponds to a 85% level of confidence.
z a/2 = 1.44
Katrina wants to estimate the proportion of adults who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adults and constructs a 95% confidence interval. Matthew also wants to estimate the proportion of adults who read at least 10 books last year. He obtains a simple random sample of 400 adults and constructs a99% confidence interval. Assuming both Katrina and Matthew obtained the same point estimate, whose estimate will have the smaller margin of error? Justify your answer.
Matthew's estimate will have the smaller margin of error because the larger sample size more than compensates for the higher level of confidence.
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=921 and x=558 who said "yes." Use a 95% confidence level.
a) Find the best point estimate of the population proportion p. . 606 b) Identify the value of the margin of error E. E=0.032 c) Construct the confidence interval. .574<p<. 637 d) Write a statement that correctly interprets the confidence interval. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.