Exam 2 Due date 112215 or before The height of the probabili

Exam 2

Due date: 11/22/15 or before

The height of the probability density function f(x) of the uniform distribution defined on the interval [a,b] is _____________.

1/(b – a) between a and b, and zero otherwise

(b – a)/2 between a and b, and zero otherwise

(a + b)/2 between a and b, and zero otherwise

1/(a + b) between a and b, and zero otherwise

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. Find the mean and standard deviation of the waiting time.

115 seconds and 49.07 seconds

1.15 minutes and 0.4907 minutes

1.15 minutes and 24.08333 (minute)²

115 seconds and 2408.3333 (second)²

The time of a call to a technical support line is uniformly distributed between 2 and 10 minutes. What are the mean and variance of this distribution?

6 minutes and 2.3094 (minutes)²

6 minutes and 5.3333 (minutes)²

6 minutes and 5.3333 minutes

8 minutes and 2.3094 minutes

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

The tails get closer and closer to the x axis but never touch it.

The tails gets closer and closer to the x axis and eventually touch it.

The tails get closer and closer to the x axis and eventually cross this axis.

The tails get closer and closer to the x axis and eventually become this axis.

Find the probability P(–1.96 Z 1.96).

0.0500

0.9500

0.9750

1.9500

Which of the following is an example of a sample statistic?

Bias can occur in sampling. Bias refers to _____________________.

The division of the population into overlapping groups

The creation of strata, which are proportional to the stratum’s size

The use of cluster sampling instead of stratified random sampling

The tendency of a sample statistic to systematically over- or underestimate a population parameter

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. The probability that the sample mean is between 25 and 30 school days is ___________.

0.0228

0.0918

0.8854

0.9082

A local company makes snack size bags of potato chips. Each day, the company produces batches of 400 snack size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. However, due to imperfect technology, the actual amount placed in a given bag varies. Assume the amount placed in each of the 400 bags is normally distributed and has a standard deviation of 0.1 ounces. What is the probability that a sample of 40 bags has an average weight of at least 2.02 ounces?

0.0150

0.0918

0.1038

0.4207

What is the purpose of calculating a confidence interval?

To provide a range of values that has a certain large probability of containing the sample statistic of interest

To provide a range of values that, with a certain measure of confidence, contains the sample statistic of interest

To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest

To provide a range of values that has a certain large probability of containing the population parameter of interest

What is the most typical form of a calculated confidence interval?

Point estimate ± Standard error

Point estimate ± Margin of error

Population parameter ± Standard error

Population parameter ± Margin of error

We draw a random sample of size 25 from the normal population with the variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?

[11.2600, 13.7400]

[11.3835, 13.6165]

[11.7019, 13.2981]

[11.7793, 13.2207]

The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120. The revenue on each of the last 25 days is noted, and the average is computed as $550. A 95% confidence interval is constructed for the population mean revenue. If the data from the last 40 days had been used, then the resulting 95% confidence intervals would have been _____________________.

Wider, with a larger probability of reporting an incorrect interval

Wider, with the same probability of reporting an incorrect interval

Narrower, with a larger probability of reporting an incorrect interval

Narrower, with the same probability of reporting an incorrect interval

Construct a 99% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a recent poll of 300 residents, 98 supported candidate B and 58 supported candidate C.

[0.4057, 0.5543]

[0.4130, 0.5470]

[0.4779, 0.4821]

[0.4781, 0.4819]

In general, the null and alternative hypotheses are __________.

Additive

Correlated

Multiplicative

Mutually exclusive

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies that are born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician’s claim.

For a given sample size , ________________.

Decreasing the probability of a Type I error will increase the probability of a Type II error

Decreasing the probability of a Type I error will decrease the probability of a Type II error

Changing the probability of a Type I error will have no impact on the probability of a Type II error

Increasing the probability of a Type I error will increase the probability of a Type II error as long as is known

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is ____________.

A school teacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the critical value(s) is (are) _______.

Solution

The height of the probability density function f(x) of the uniform distribution defined on the interval [a,b] is _____________.

1/(b – a) between a and b, and zero otherwise

Mean=(30+200)/2=115

Standard deviation=1/12*(b-a)=(200-30)/12=49.07

Mean=(2+10)/2=6

Standard deviation=1/12*(b-a)=(10-2)/12=2.3

P(–1.96 Z 1.96)=0.95

Bias can occur in sampling. Bias refers to The tendency of a sample statistic to systematically over- or underestimate a population parameter

Standard deviation of sample mean= population sd/n

The purpose of calculating CI is To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest

The typical form of CI is: Point estimate ± Margin of error

If the data from the last 40 days had been used, then the resulting 95% confidence intervals would have been Wider, with the same probability of reporting an incorrect interval.

In general, the null and alternative hypotheses are Mutually exclusive