Statistics
1 Pollsters often use randomly selected digits between 0 and 9 to generate parts of telephone numbers to be called. What is the distribution of such randomly selected digits? If a pollster repeats the process of randomly generating 50 digits and finding the mean, what is the distribution of the resulting sample means?
What is the distribution of the randomly selected digits between 0 and 9?
Single-peaked
Normal
Uniform
Left-skewed
If a pollster repeats the process of randomly generating 50 digits and finding the mean, what is the distribution of the resulting sample means?
Normal
Approximately normal
Left-skewed
Approximately left-skewed
2. Assume that cans are filled so that the actual amounts have a mean of 15.00 ounces. A random sample of 36 cans has a mean amount of 15.46 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 15.00 ounces and a standard deviation of 0.05 ounce.
a. How many standard deviations is the sample mean from the mean of the distribution of sample means?
standard deviations (Round to the nearest tenth as needed.)
b. In general, what is the probability that a random sample of size 36 has a mean of at least 15.46 ounces?
A.
The probability is very small (such as 0.01% or smaller).
B.
The probability is very large (such as 99.99% or greater).
C.
The probability is about 9.2%.
c. Does it appear that consumers are being cheated?
Yes
No
3. Suppose that, in a suburb of 12,388 people, 6,544 people moved there within the last five years. You survey 450 people and find that 218 of the people in your sample moved to the suburb in the last five years.
a. What is the population proportion of people who moved to the suburb in the last five years?
The population proportion is
(Round to the nearest thousandth as needed.)
b. What is the sample proportion of people who moved to the suburb in the last five years?
The sample proportion is
(Round to the nearest thousandth as needed.)
c. Does your sample appear to be representative of the population?
Yes
No
D.
b. Identify the probability of each sample and describe the sampling distribution of sample means.
Each sample has probability
.
(Type an integer or a simplified fraction.)
c. Find the mean of the sampling distribution.=
(Type an integer or decimal rounded to two decimal places as needed.)
d. Is the mean of the sampling distribution [from part (c)] equal to the mean of the population of the three listed values? If so, are those means always equal?
A.
No, the sample mean is not equal to the mean of the population. These means are not always equal, because the mean is an unbiased estimator.
B.
Yes, the sample mean is equal to the mean of the population. These means are always equal, because the mean is a biased estimator.
C.
No, the sample mean is not equal to the mean of the population. These means are not always equal, because the mean is a biased estimator.
D.
Yes, the sample mean is equal to the mean of the population. These means are always equal, because the mean is an unbiased estimator.
Click to select your answer(s).
.
5. Assume that population means are to be estimated from the samples described. Use the sample results to approximate the margin of error and 95% confidence interval. Sample size equals=1, 078 sample mean equals=$46,262 sample standard deviation equals=$22 000
The margin of error is
$
(Round to the nearest dollar as needed.)
Find the 95% confidence interval.
$ <µ<$
(Round to the nearest dollar as needed.)
6 Assume that you want to construct a 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval. The sample standard deviation is given below. Margin of error equals=$5, standard deviation equals=$24
The required sample size is
(Round up to the nearest whole number as needed.)
7. One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.27 hour is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
The required sample size is
(Round up to the nearest whole number.)
8 A new IQ test is designed so that the mean is 100 and the standard deviation is 13 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of residents of a state. We want to be 95% confident that our sample mean is within 2 IQ points of the true mean. Assume that s equals=13 and determine the required sample size.
The minimum sample size is
nothing.
(Round up to the nearest whole number as needed.)
9 Estimate the minimum sample size needed to achieve the margin of error E=0.0370.
The minimum sample size is
(Round up to the nearest integer.)
10 A study done by researchers at a university concluded that 50% of all student athletes in this country have been subjected to some form of hazing. The study is based on responses from 1,400 athletes. What are the margin of error and 95% confidence interval for the study?
The margin of error is
(Round to the nearest thousandth as needed.)
Find the 95% confidence interval.
<p<
(Round to the nearest thousandth as needed.)
11. A research institute conducted clinical trials of a method designed to increase the probability of conceiving a boy. Among 161 babies born to parents using the method,140 were boys. Identify the margin of error and the 95% confidence interval for these clinical trials.
The margin of error is
(Round to three decimal places as needed.)
Construct the 95% confidence interval.
<p<
(Round to three decimal places as needed.)
