TRUE OR FALSE

1._____The arithmetic meanis the sum of the observations divided by the total number of observations.

2._____There are always as many values above the mean as below it.

3._____The standard deviationis the positive square root of the variance. It is a measure of dispersion in the same units as the original data.

4._____According the Empirical Rule, about 68 percent of the observations lie within plus and minus two standard deviations of the mean.

5._____If only one of several events can occur at a time, we refer to the events as being mutually exclusive events.

6._____The probabilitythat you would assign to the likelihood that the Tampa Bay Buccaneers will be in the Superbowl this season must be between 1 and 10.

7._____About 95 percent of the area under the normal curve is within plus one and minus one standard deviation of the mean.

8._____The normal probability distribution is generally deemed a good approximation for the binomialprobability distribution when np and n(1-p) are both five or greater.

9._____A samplingerror is the difference between the sample statistic and the population parameter.

10.____A 95% confidence intervaltells us that we are 95% sure the population mean will fall outside the interval.

MULTIPLE CHOICE

11.Which measures of central tendencywill the sum of the deviations of each value from that average always be zero?

a. Mode

b. Arithmetic Mean

c. Median

d. Geometric mean

e. None of the above.

12.In a symmetric distribution, the mean, median, and mode:

a. are all equal.

b. the mean is always the smallest value.

c. the mean is always the largest value.

d. mean is never equal to the median.

e. none of the above.

13.If there is an odd number of observations in a set of ungrouped data, the median is located at:

a. n.

b. n/3.

c. (n+1)/2.

d. none of the above.

14.According to Empirical Rule, what percent of the observations lie within plus and minus 1 standard deviations of the mean?

a. About 99 percent

b. About 95 percent

c. About 68 percent

d. cannot compute, it depends on the shape of the distribution.

15.A Z score is the result of the difference between X and the population mean divided by :

a. sample mean.

b. population standard deviation.

c. sample variance.

d. none of the above.

16.A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. If the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 and 900 hours?

a. 95 percent

b. 68 percent

c. 34 percent

d. 99.7 percent

e. cannot be determined from the information given.

17.What proportion of the area under a normal curve is to the right of a z-score of zero?

a. 0 percent

b. 50 percent

c. 100 percent

d. 34 percent

e. none of the above are correct.

18.The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. what is the area between 415 pounds and the mean of pounds?

a. about 0.5000

b. about 0.1983

c. about 0.8750

d. about 0.3413

e. none of the above.

19. Which of the following is not a probability sample?

a. Panel.

b. Simple Random.

c. Cluster.

d. Systematic.

e. None of the above.

20. For a given confidence interval, what is the interpretation of a 96% confidence level?

a. 96% chance that the given interval includes the true value of the population parameter.

b. Approximately 96 out of 100 such intervals would include the true value of the population parameter.

c.4% chance that the given interval does not include the true value of the population parameter

d. Both “a” and “c” are true.

d. none of the above is correct.

When doing the problems show as much of your work as you can. You may receive partial credit for all work attempted.

Question #21

The Savings and Loan where you work has asked you to compare its new advertising campaign to the campaign it had been using. You have gathered sample data on the number of accounts for both the old and the new campaigns. The data are as follows:

OLD : 40, 28, 35, 38, 31, 42, 26, 44, 29, 43

NEW:29, 26, 31, 26, 28, 31, 19, 21, 27, 30

Determine for each of the two advertising campaigns the following:

(SHOW YOUR WORK INCLUDING FORMULAS)

a. Calculate the mean, median, and the modefor each group of data.

b. Calculate the variance and the standard deviation for each group of data. (Be sure to indicate which formula you are using)

c. Calculate a 95% Confidence Interval for the two sets of data. What do these Confidence Intervalstell us? (8 points)

d. Which of the two campaigns is the more successful? Justify your decision.

Question #22

An executive at Hughes drives from his home to work every day. The driving times are normally distributed with a mean of 35 minutes and a standard deviation of 8 minutes.

a. In what percent of the days will it take him 30 or fewer minutes to reach his office?

b. What percent of the days will it take between 40 and 50 minutes?

c. What percent of days will it take him between 30 and 45 minutes?

d. How long will the longest 10% of the trips take?

Please see attached file

TRUE OR FALSE (3 points each)

1.__True___ The arithmetic mean is the sum of the observations divided by the total number of observations.

2._False____ There are always as many values above the mean as below it.

There are always as many values above the median as below it.

3._True____ The standard deviation is the positive square root of the variance. It is a measure of dispersion in the same units as the original data.

4._False____ According the Empirical Rule, about 68 percent of the observations lie within plus and minus two standard deviations of the mean.

According the Empirical Rule, about 68 percent of the observations lie within plus and minus one standard deviations of the mean.

5._True____ If only one of several events can occur at a time, we refer to the events as being mutually exclusive events.

6._False____ The probability that you would assign to the likelihood that the Tampa Bay Buccaneers will be in the Superbowl this season must be between 1 and 10.

Probability can never be more than 1.

7._False____ About 95 percent of the area under the normal curve is within plus one and minus one standard deviation of the mean.

About 95 percent of the area under the normal curve is within plus one and minus two standard deviation of the mean.

8._False____ The normal probability distribution is generally deemed a good approximation for the binomial probability distribution when np and n(1-p) are both five or greater.

9._True____ A sampling error is the difference between the sample statistic and the population parameter.

10._False___ A 95% confidence interval tells us that we are 95% sure the population mean will fall outside the interval.

A 95% confidence interval tells us that we are 95% sure the population mean will fall inside the interval.

MULTIPLE CHOICE (3 points each)

11 Which measures of central tendency will the sum of the deviations of each value from that average always be zero?

a. Mode

b. Arithmetic Mean

c. Median

d. Geometric mean

e. None of the above.

Answer: b. Arithmetic Mean

12 In a symmetric distribution, the mean, median, and mode:

a. are all equal.

b. the mean is always the smallest value.

c. the mean is always the largest value.

d. mean is never equal to the median.

e. none of the above.

Answer: a. are all equal.

13 If there is an odd number of observations in a set of ungrouped data, the median is located at:

a. n.

b. n/3.

c. (n+1)/2.

d. none of the above.

Answer: c. (n+1)/2.

14 According to Empirical Rule, what percent of the observations lie within plus and minus 1 standard deviations of the mean?

a. About 99 percent

b. About 95 percent

c. About 68 percent

d. cannot compute, it depends on the shape of the distribution.

Answer: c. About 68 percent

15 A Z score is the result of the difference …

Answers Multiple Choice Questions and numericals on confidence interval and probability.