WorksheetsConfidence Intervals
Total questions: 25
Worksheet time: 1hrs 17mins
Name
Class
Date
1.
Which z-value is used for a 95% confidence interval?
a)
1.65
b)
1.96
c)
2.58
d)
2.33
2.
Given the same mean, SD, and sample size, a confidence interval of 80% would be wider than a confidence interval of 90%
a)
True
b)
False
3.
In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a sample standard deviation of $950. Construct a 99% confidence interval for the repair cost.
a)
(1069.77, 2530.23)
b)
(1077.13, 2522.87)
c)
(1167.15, 2432.85)
d)
None of these.
4.
A sample of 40 people owned an average of 1.35 apple products. It is known from a previous study that the population standard deviation of apple product ownership is 0.63 products. Construct a 95% confidence interval.
a)
(1.11, 1.58)
b)
(1.15, 1.55)
c)
(1.19, 1.51)
d)
(1.09, 1.61)
5.
A sample of 30 women finds the mean height to be 62.3 in and the standard deviation to be 1.5 in. Find the margin of error of women's heights with a 95% CL.
a)
1.699
b)
0.56
c)
0.537
d)
19.325
6.
A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.
a)
90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144
b)
We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
c)
There is a 90% chance that CEOs in the electronics industry have salaries that fall between $139,048 to $154,144
d)
We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.
7.
A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Based on this sample, a 90% confidence interval for the mean improvement in test scores for all sixth-graders in the city taking this course is found to be (12.6, 14.8). Which of the following are the sample mean and margin of error on which this interval is based?
a)
Sample Mean = 13.7; Margin of Error = 1.1
b)
Sample mean = 13.7; Margin of Error = 2.2
c)
Sample mean is unknown; Margin of Error = 2.2
8.
A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Based on this sample, a 90% confidence interval for the mean improvement μ in test scores for all sixth-graders in the city taking this course is found to be (12.6, 14.8). Which one of the following is a correct interpretation of this confidence interval?
a)
Ninety percent of the 85 sixth-graders in the sample improved their reading comprehension scores by 12.6 to 14.8 points.
b)
The probability is 0.90 that the true mean improvement in reading comprehension is between 12.6 and 14.8.
c)
We are 90% confident that the true improvement in reading comprehension scores is captured by the interval 12.6 to 14.8.
9.
Agricultural researchers plant 100 plots with a new variety of corn and measure the mean yield for these plots in bushels per acre. They treat the 100 plots as a simple random sample of possible plots of corn (as researchers often do) and report a 95% confidence interval for the mean corn yield of (128.4, 131.6) bushels per acre. Which of the following is a correct interpretation of the 95% confidence level?
a)
We are 95% confident that the true mean yield for this new variety of corn is captured by the interval (128.4, 131.6) bushels per acre
b)
If many intervals were constructed this way from many independent sets of 100 plots, 95% of the intervals would capture the true mean corn yield.
c)
If many intervals were constructed this way from many independent sets of 100 plots, 95% of the time the true mean corn yield would be in the interval (128.4, 131.6) bushels per acre.
10.
A radio talk show host is interested in the proportion p of adults in his listening area who think that the drinking age should be lowered to 18. To find this proportion, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to 18?” He asks listeners to phone in and vote “yes” or “no” depending upon their opinions. Of 200 people who phone in, 140 answer “yes.” The standard error of the sample proportion of “yes” votes among those who phone in is
a)
.21
b)
.032
c)
.00105
11.
A random sample of size n is collected from a Normally distributed population with standard deviation σ. Using these data, a confidence interval is computed for the mean of the population. Which of the following actions would produce a new confidence interval with a smaller width (smaller margin of error), assuming that the same data were used?
a)
Using a higher confidence level
b)
Using a lower confidence level
c)
Using a smaller sample size n
12.
An inspector monitors large truckloads of potatoes to determine the proportion p of potatoes with major defects before the potatoes are used to make potato chips. She intends to compute a 95% confidence interval for p. To do so, she selects a simple random sample of 50 potatoes from a truckload of more than 2000 potatoes. Suppose that only 2 of the 50 potatoes sampled are found to have major defects. Which one of the following assumptions for inference about a proportion using a confidence interval is violated?
a)
Large counts.
b)
10% condition.
c)
There are not violations.
13.
One hundred rats with mothers that were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. At the outset, the maze required the rats to make a choice between going left and going right. Eighty of the rats went right when running the maze for the first time. Assume that the 100 rats can be considered an SRS from the population of all rats born to mothers who were exposed to high levels of tobacco smoke during pregnancy. (Note that this assumption may or may not be reasonable, but researchers often assume that lab rats are representative of large populations, since they are often bred to have uniform characteristics.) Let p be the proportion of rats in this population that would go right when running the maze for the first time. A 90% confidence interval for p is
a)
0.8 ± 0.040.
b)
0.8 ± 0.078.
c)
0.8 ± 0.066.
14.
To assess the accuracy of a kitchen scale, a standard weight, known to weigh 1.000 gram, is weighed a total of n times, and the mean of the n weight measurements is computed. (If a 90% confidence interval for the mean calculated from these measurements does not contain 1.000, the scale is deemed inaccurate.) Suppose the scale readings are Normally distributed and that similar scales are known to measure such weights with a standard deviation of σ = 0.01 gram. Which of the following is the smallest value of n that will produce a 90% confidence interval with a margin of error of at most 0.001 grams?
a)
17
b)
271
c)
385
15.
Which one of the following statements is true about Student's t distribution?
a)
The density curve of the t distribution is symmetric and centered at the true mean of the population.
b)
The density curve of the t distribution has heavier “tails” than the density curve of the standard Normal distribution.
c)
The density curve of the t distribution more closely resembles the density curve of the standard Normal distribution when the number of degrees of freedom is small.
16.
The heights (in inches) of adult males on a small Pacific Island are believed to be Normally distributed with an unknown mean μ. The average height of a random sample of 25 adult males from the island is found to be 69.72 inches, with a sample standard deviation of s = 4.15 inches. A 99% confidence interval for μ is
a)
69.72 ± 2.32.
b)
69.72 ± 2.07.
c)
69.72 ± 11.61
17.
You are thinking of using a t procedure to construct a 95% confidence interval for the unknown mean μ of a population for a random sample taken from the population. You suspect that the distribution of the population is not Normal and may in fact be moderately skewed. Which of the following statements is then correct?
a)
You should not use the t procedure, since the population does not have a Normal distribution.
b)
You can use the t procedure provided that n>30 .
c)
You can use the t procedure regardless of the sample size since t procedures are robust against non-Normality.
18.
What is the t value associated with 90% confidence and a sample size of 15?
a)
1.341
b)
1.345
c)
1.761
d)
1.753
19.
What is the degrees of freedom equal to?
a)
n
b)
n+1
c)
1-n
d)
n-1
20.
In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a sample standard deviation of $950. Construct a 99% confidence interval for the repair cost.
a)
(1069.77, 2530.23)
b)
(1077.13, 2522.87)
c)
(1167.15, 2432.85)
d)
None of these.
21.
Thirty-five randomly selected students took the calculus final. If the sample mean was 92 and the standard deviation was 9.4, construct a 90 percent confidence interval for the mean score of all students.
a)
89.08 < μ < 94.92
b)
89.39 < μ < 94.61
c)
87.29 < μ < 96.71
d)
87.77 < μ < 96.23
22.
Find the minimum sample size needed to be 4% within the true proportion if you are 95% confident and p-hat = 0.6
a)
12
b)
961
c)
577
d)
126
23.
When the standard deviation is estimated from data, the result is called the ... of the statistic.
a)
standard error
b)
confidence interval
c)
sample mean
d)
population mean
24.
Find the t* value for a 99% confidence interval with a sample of 23 people.
a)
1.714
b)
1.711
c)
2.064
d)
None of these.
25.
A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...
a)
The sample size is too small for a z-distribution
b)
Clarity ratings for the entire bacth are normally distributed.
c)
The t-distribution will create a narrower interval than z.
d)
The standard deviation for the batch is unknown.
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