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- From: Mathematics, Statistics and Probability
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Question 1 4 points Save
As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.
True
False
Question 2 4 points Save
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?
18.750
2.500
1.875
0.750
Question 3 4 points Save
Which of the following is TRUE about the sampling distribution of the sample mean?
The mean of the sampling distribution is µ.
The standard deviation of the sampling distribution is always sigma, .
The shape of the sampling distribution is always approximately normal.
All of the above are true.
Question 4 4 points Save
If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.
True
False
Question 5 4 points Save
The amount of time it takes to complete an examination has a skewed-left distribution with a mean of 65 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.
True
False
Question 6 4 points Save
A sampling distribution is a probability distribution for a statistic.
True
False
Question 7 4 points Save
The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would
increase the sample size to 200.
increase the sample size to 400.
decrease the sample size to 50.
decrease the sample to 25.
Question 8 4 points Save
If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4 and it is assumed that the amount of gasoline purchased per car is symmetric, there is about a 68% chance that a random sample of 16 cars will have a sample mean between $14 and $16.
True
False
Question 9 4 points Save
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for p is 0.59 ± 0.07. Interpret this interval.
We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.
95% of the students get between 52% and 66% of their tuition paid for by financial aid.
We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid.
We are 95% confident that 59% of the students are on some sort of financial aid.
Question 10 4 points Save
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: the sample mean = $50.50 and sample variance = 400. Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for µ (mu)?
Approximately normal with a mean of $50.50
A standard normal distribution
A t distribution with 15 degrees of freedom
A t distribution with 14 degrees of freedom
Question 11 4 points Save
A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to a new store. Fifteen credit card accounts were randomly sampled and analyzed with the following results: sample mean=$50.50 and sample variance=121. Construct a 95% confidence interval for the average amount its credit card customers spent on their visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution (that is, the sample variance equals the population variance).
$50.50 ± 1.96*121
$50.50 ± 1.96*(sqrt(121))
$50.50 ± 1.96/(sqrt(121))
$50.50 ± 1.96*(sqrt(121))/(sqrt(15))
Question 12 4 points Save
As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, the sample mean=19.8 and the sample variance =25. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.
19.8 ± 1.249
18.2 ± 5.24
15.4 ± 21.5
20.5 ± 7.25
Question 13 4 points Save
The t distribution
assumes the population is normally distributed.
approaches the normal distribution as the sample size increases.
has more area in the tails than does the normal distribution.
All of the above.
Question 14 4 points Save
A sample size of 5 provides a sample mean of 9.6. If the population variance is known to be 5 and the population distribution is assumed to be normal, the lower limit for a 92% confidence interval is 7.85.
True
False
Question 15 4 points Save
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?
n = 1,844
n = 1,784
n = 1,503
n = 1,435
Question 16 4 points Save
A librarian asked his assistant for an estimate of the mean number of books checked out each day. The assistant estimated from 740 to 920 books per day. What is an efficient, unbiased point estimate of the number of books checked out each day?
740
830
920
None of the above.
Question 17 4 points Save
If a test of hypothesis has a Type I error probability, ? = 0.01, we mean
If the null hypothesis is true, we do not reject it 1% of the time.
If the null hypothesis is true, we reject it 1% of the time.
If the null hypothesis is false, we do not reject it 1% of the time.
if the null hypothesis is false, we reject it 1% of the time.
Question 18 4 points Save
If the Type I error, ? for a given test is to be decreased, then for a fixed sample size:
the Type II error (?) will also decrease.
the Type II error (?) will increase.
the power of the test will increase.
a one-tailed test must be utilized.
Question 19 4 points Save
If the p-value is less than ? in a two-tailed test, then:
the null hypothesis should not be rejected.
the null hypothesis should be rejected.
a one-tailed test should be used.
no conclusion should be reached.
Question 20 4 points Save
Which of the following would be an appropriate null hypothesis?
The mean of a population is equal to 55.
The mean of a sample is equal to 55.
The mean of a population is greater than 55.
The mean of a sample is greater than 55.
Question 21 4 points Save
A is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
significance level
critical value
test statistic
parameter
Question 22 4 points Save
Suppose we wish to test the null hypothesis H0: ? ? 47 versus H1: ? > 47. What will result if we conclude that the mean is greater than 47 when its true value really is 52?
We have made a Type I error.
We have made a Type II error.
We have made a correct decision
None of the above are correct.
Question 23 4 points Save
The symbol for the power of a statistical test is
?
1 - ?
?
1 - ?
Question 24 4 points Save
Which of the following would be an appropriate alternative hypothesis?
The mean of a population is equal to 55.
The mean of a sample is equal to 55.
The mean of a population is greater than 55.
The mean of a sample is greater than or equal to 55.
Question 25 4 points Save
The power of a test is measured by its capability of
rejecting a null hypothesis that is true.
not rejecting a null hypothesis that is true.
rejecting a null hypothesis that is false.
not rejecting a null hypothesis that is false.
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