Bana 1 Exam 3
In a restaurant, the proportion of people who order coffee with their dinner is 0.9. A simple random sample of 144 patrons of the restaurant is taken.
(a) -What is the expected value of the sampling distribution of p (bar)? (0.9) -What is the standard deviation of the sampling distribution of p (bar)? (.025) -What is the shape of the sampling distribution of p (bar)? (Normal) (b)What is the probability that the proportion of people who will order coffee with their meal is between 0.84 and 0.865? (.0726) (c)What is the probability that the proportion of people who will order coffee with their meal is at least 0.925? (.1587)
Refer to Question 12, what is the p-value associated with the hypothesis test? Round your answer to three decimal places.
.006
Refer to Questions 1 & 2 and round your answer to three decimals. The p-value is
.046
Random samples of size 800 are taken from an infinite population whose population proportion is 0.2. Find the standard deviation of the sample proportions
0.0141
Refer to Questions 8 & 9. The p-value is
0.0228
The manager of a grocery store has taken a random sample of 121 customers. The average length of time it took these 121 customers to check out was 5 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. Find the standard error of the mean.
0.091
The manager of a grocery store has taken a random sample of 289 customers. The average length of time it took these 289 customers to check out was 2 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The standard error is 0.0588. Find the margin of error, with a 0.95 probability, that the sample mean will provide.
0.115
In a local university, 66% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. We know that the standard error of the proportion is 0.0530. Find the probability that the sample proportion (the proportion living in the dormitories) is between 0.64 and 0.67.
0.2220
A sample of 54 observations will be taken from an infinite population. The population proportion equals 0.85. Find the probability that the sample proportion will be between 0.8127 and 0.8431.
0.2222
A population has a mean of 400 and a standard deviation of 25. A sample of 100 observations will be taken. Find the probability that the sample mean will be greater than 401.
0.3446
A population has a standard deviation of 10. If a sample of size 25 is selected from this population, what is the probability that the sample mean will be within ±2 of the population mean?
0.6827
Five hundred people were asked whether gun laws should be more stringent. Four hundred said "yes," and 100 said "no." Find the point estimate of the proportion in the population who will respond "yes."
0.8
A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. Find the probability that the sample proportion will be greater than 0.73.
0.9998
Refer to Question 8. The value of the test statistic is
2.0
Read the t statistic from the t distribution table and choose the correct answer. For a two-tailed test with a sample size of 19 and using 𝛼 = 0.05, find t.
2.101
Find the critical value of t for a two-tailed test with 11 degrees of freedom using 𝛼 = 0.05.
2.201
Random samples of size 36 are taken from an infinite population whose mean and standard deviation are 280 and 12, respectively. The distribution of the population is unknown. Find the mean and the standard error of the mean.
280 and 2
A population consists of 14 items. What is the number of different simple random samples of size 3 that can be selected from this population
364
The manager of a grocery store has taken a random sample of 169 customers. The average length of time it took these 169 customers to check out was 5 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. The margin of error is 0.151. Find the 95% confidence interval for the true average checkout time (in minutes).
4.849 to 5.151
From a group of 11 students, we want to select a random sample of 5 students to serve on a university committee. How many combinations of random samples of 5 students can be selected
462
A population has a standard deviation of 36. A random sample of 124 items from this population is selected. The sample mean is determined to be 325. What is the margin of error at 95% confidence?
6.34
Consider the following hypothesis test. H0: μ ≥ 55 Ha: μ < 55
A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use 𝛼 = 0.01. x = 54 and s = 5.3 Find the value of the test statistic. (Round your answer to three decimal places.) -1.132 Find the p-value. (Round your answer to four decimal places.) p-value = 0.1326 State your conclusion:Do not reject H0. There is insufficient evidence to conclude that μ < 55. x = 53 and s = 4.6 Find the value of the test statistic. (Round your answer to three decimal places.) -2.609 Find the p-value. (Round your answer to four decimal places.) p-value = 0.0066 State your conclusion:Reject H0. There is sufficient evidence to conclude that μ < 55. x = 56 and s = 5.0 Find the value of the test statistic. 1.2 Find the p-value. (Round your answer to four decimal places.) p-value = 0.8809 State your conclusion:Do not reject H0. There is insufficient evidence to conclude that μ < 55.
Using the critical value approach and 𝛼 = 0.05, test the hypotheses.
Determine the critical value(s) for this test. (Round your answer(s) to two decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic≤-1.96 test statistic≥1.96 What is your conclusion? Do not reject H0. There is insufficient evidence to conclude that the mean of all account balances is significantly different from $1,100.
A sample of 64 account balances from a credit company showed an average daily balance of $1,130. The standard deviation of the population is known to be $160. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1,100.
Develop the appropriate hypotheses (in dollars) for this problem. (Enter != for ≠ as needed.) H0: μ=1100 Ha: μ!=1100 Compute the test statistic: 1.5 Compute the p-value. (Round your answer to four decimal places.). p-value = .1336
Using the p-value approach and 𝛼 = 0.05, test the above hypotheses. What is your conclusion?
Do not reject H0. There is insufficient evidence to conclude that the mean of all account balances is significantly different from $1,100.
Consider the following hypothesis test. H0: μ = 15Ha: μ ≠ 15
Find the value of the test statistic. (Round your answer to two decimal places.) -2.10 Find the p-value. (Round your answer to four decimal places.) p-value = .0357 At 𝛼 = 0.05, state your conclusion: Reject H0. There is sufficient evidence to conclude that μ ≠ 15. State the critical values for the rejection rule. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic≤-1.96 test statistic≥1.96
The company identified in Chapter 8, Statistics in Practice is
Food Lion
The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is
H₀: the average life expectancy is less than or equal to 40,000; Hᴀ: the average life expectancy is greater than 40,000
The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the growing economy has led to an increase in the average work week. To test the validity of this belief, the hypotheses are
H₀: the population mean is less than or equal to 40.1; Hᴀ: the population mean is greater than 40.1
A machine is designed to fill toothpaste tubes with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling.
H₀:the population mean equals 5.8; Hᴀ:the population mean does not equal 5.8
Which of the following statements about cluster sampling is false
It generally requires a smaller total sample size than simple random sampling.
The company identified in Chapter 9, Statistics in Practice is
John Morrell & Company
The company identified in Chapter 7, Statistics in Practice is
MeadWestvaco
As the sample size becomes larger, the sampling distribution of the sample mean approaches a
Normal distribution
If a hypothesis test leads to the rejection of the null hypothesis,
a Type I error may have been committed
An interval estimate is a range of values used to estimate
a population parameter
Cluster sampling is
a probability sampling method
Whenever the population has a normal probability distribution, the sampling distribution of the sample mean is a normal probability distribution for
any sample size
When the level of confidence decreases, the margin of error
becomes smaller
If the probability of a Type I error (𝛼) is 0.1, then the probability of a Type II error (β)
cannot be computed
The power curve provides the probability of
correctly rejecting the null hypothesis.
If the level of significance of a hypothesis test is raised from 0.025 to 0.05, the probability of a Type II error will
decrease.
The Statistics in Practice example in Chapter 7 identifies an application concerned with
forest management
As the absolute value of the test statistic becomes larger, the p-value
gets smaller.
Chapter 9's primary focus is
hypothesis tests
In hypothesis tests about a population proportion, p0 represents the
hypothesized population proportion
For a given level of Type I error, if we want to decrease the level of Type II error, the sample size must
increase
It is impossible to construct a frame for a(n)
infinite population
Chapter 8 focuses on
interval estimation
The Statistics in Practice example in Chapter 8 identifies an application concerned with
inventory evaluation
Which of the following is an example of nonprobability sampling
judgment sampling
In the hypothesis testing procedure, alpha is the
level of significance.
The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the
margin of error
The p-value
must be a number between zero and 1
In computing the standard error of the mean, the finite population correction factor is used when
n/N > 0.05
Convenience sampling is an example of
nonprobability sampling
A random sample of 100 people was taken. Eighty-one of the people in the sample favored Candidate A. We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 79%. We know that the p-value is 0.3117. At the 0.05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is
not significantly greater than 79%.
As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever
np ≥ 5 and n(1 - p) ≥ 5
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
p-value ≤ alpha
What is the single numerical value used as an estimate of a population parameter known as
point estimate
The purpose of statistical inference is to provide information about the
population based upon information contained in the sample.
When the null hypothesis is not rejected, it is
possible a Type II error has occurred.
The Statistics in Practice example in Chapter 9 identifies an application concerned with
product preference
In stratified random sampling
randomly selected elements within each of the strata form the sample
Refer to Question 10. If alpha is .05, the correct conclusion is
reject the null hypothesis
Refer to Question 13. If alpha is .05, the correct conclusion is
reject the null hypothesis
Refer to Question 3. If alpha is .05, the correct conclusion is
reject the null hypothesis
What is a subset of a population selected to represent the population called
sample
Chapter 7 focuses on
sampling
The probability distribution of all possible values of the sample proportion p (bar) is the
sampling distribution of p (bar)
The probability distribution of the sample mean is called the
sampling distribution of the mean
The absolute value of the difference between the point estimate and the population parameter it estimates is the
sampling error
More evidence against H₀ is indicated by
smaller p-values.
What is the standard deviation of x (bar) called?
standard error of the mean
As the sample size increases, the
standard error of the mean decreases
A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is
systematic sampling.
The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed an average price of $210,000. It is known that the standard deviation of the population is $36,000. Has the price decreased? The correct null hypothesis for this problem is
the average house price is greater than or equal to $220,000
A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters. The population standard deviation is 0.44 centimeters.
the average length equals 6.0 centimeters
The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,300 per day. From past information, it is known that the standard deviation of the population is $1,200. The correct null hypothesis for this problem is
the daily average is less than or equal to 8000
In hypothesis testing, the tentative assumption about the population parameter is
the null hypothesis
For a given sample size in hypothesis testing,
the smaller the Type I error, the larger the Type II error will be.
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the
width of the confidence interval to increase.
Which of the following is the largest data set size
yottabyte
In a lower tail hypothesis test situation, the p-value is determined to be 0.1. If the sample size for this test is 46, what is the value of the t statistic?
−1.301
For a lower tail hypothesis test with a sample size of 15 and a 0.10 level of significance, what is the critical value of the test statistic t?
−1.345
