CF QUESTION:

18. The average annual total return for U.S. Diversified Equity mutual funds from 1999 to 2003 was 4.1% (Business Week, January 26, 2004). A researcher will like to conduct a hypothesis test to see whether the returns for mid-cap growth funds over the same period are significantly different from the average for U.S. Diversified Equity Funds.

a. Fromulate the hypothesis that can be used to determine whether the mean annual return for mid-cap gorwth funds differ from the mean for U.S. Diversified Equity funds.

b. A sample of 40 mid-cap growth funds provides a mean return of x = 3.4%. Assume the population standard deviation for mid-cap growth funds is known from previous studies to be o = 2%. Use the sample results to compute the test statistic and p-value for the hypothesis test. (the x has the little line on the top)

c. At a = .05, what is your conclusion?

*Consider the following to answer the next *two questions:

The administration of a large university is interested in learning about the types of wellness programs that would interest its employees. To do this, they plan to survey a sample of their employees.

01. Suppose that there are five categories of employees (administration, faculty, professional staff, clerical and maintenance) and the university decides to randomly select ten individuals from each category. This sampling plan is called

A. Simple Random Sampling.

B. Stratified Sampling.

C. Cluster Sampling.

D. Systematic Sampling.

E. Convenience Sampling.

02. Suppose that the university randomly selects a school (e.g., the Business School) and surveys all of the individuals (administration, faculty, professional staff, clerical and maintenance) who work in that school. This sampling plan is called

A. Simple Random Sampling.

B. Stratified Sampling.

C. Cluster Sampling.

D. Systematic Sampling.

E. Convenience Sampling.

03. To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day. This sampling plan is called

A. random

B. stratified

C. systematic

D. cluster

E. convenience

04. Suppose that a company has an alphabetized list of regular customers who belong to their rewards program. They plan to survey a sample of 120 of those customers. After randomly selecting a customer on the list, every 25th customer from that point on is chosen to be in the sample. This sampling plan is called

A. Simple Random Sampling.

B. Stratified Sampling.

C. Cluster Sampling.

D. Systematic Sampling.

E. Convenience Sampling.

*Consider the following to answer the next *two questions:

A recent survey of local cell phone retailers showed that of all cell phones sold last month, 64% had a camera, 28% had a music player and 22% had both.

05. The probability that a cell phone sold last month had a camera or a music player is

A. 0.26

B. 0.70

C. 0.92

D. 0.30

E. 0.22

06. The probability that a cell phone sold last month did not have either a camera or a music player is

A. 0.26

B. 0.70

C. 0.92

D. 0.30

E. 0.22

07. Consider the Standard Normal distribution. Find P(-0.73 < z < 2.21)

A. -0.7537

B. 0.9987

C. 0.7534

D. 0.7537

E. none of the above

08. Consider the Standard Normal distribution. Find the probability P(z > 0.59)

A 0.7224

B 0.2190

C 0.2224

D 0.2776

E None of the above

09. Consider the Standard Normal distribution. Find the probability that z is less than -1.82.

A. 0.0351

B. -0.0344

C. 0.0344

D.0.9656

E. none of the above

10. Find the value of z such that the area to the left of z is 70% of the total area under the standard normal curve.

A. 0.53

B. 0.52

C. -0.52

D. -0.53

E. None of the above

11. Find the value of z such that the area between –z and +z is 98% of the total area under the standard normal curve.

A. 1.645

B. 1.96

C. 2.32

D. 2.33

E. None of the above

12. The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. Assuming a normal distribution, what is the probability that a family spends less than $410 per month?

A. 0.1151

B. -0.1151

C. 0.8849

D. -0.8461

E. none of the above

13. To construct a **normal distribution**, the measurements needed are

A the mean and the median

B the mode and the standard deviation

C the median and the standard deviation

D the standard deviation and the variance

E none of the above

14. Which of the following is not a property of the normal distribution?

A. It’s continuous

B. It is generated by a discrete random variable

C. It’s bell-shaped

D. It’s unimodal

E. The curve never touches the horizontal axis.

15. At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of 4 minutes. What percent of new machine set ups take more than 30 minutes?

A 97.72%

B 22.80%

C 2.28%

D 52.28%

E none of the above

16. The scores on a certain test are normally distributed with mean 61 and standard deviation 3. What is the probability that a sample of 100 students will have a mean score more than 61.3?

A. 0.4602

B. 0.3413

C. 0.8413

D. 0.1587

E. none of the above

17. A random sample of 66 observations was taken from a large population. The population proportion is 12%. The probability that the sample proportion will be more than 17% is

A. 0.0568

B. 0.8944

C. 0.1056

D. 0.4222

E. None of the above

18. According to a recent survey, about 33% of Americans polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed at a local supermarket. Which of the following statements is (are) true about the sampling distribution of the sample proportion?

A. The sampling distribution can be described by the normal model.

B. The mean of the sampling distribution is 0.33.

C. The standard deviation of the sampling distribution is 0.0701.

D All of the above

E Only A and B

19. The 95% confidence interval of people who hate broccoli was found to be (7.4%, 13%). The sample size was 1000. Which of the following is the correct interpretation?

A. The percentage of people who hate broccoli is between 7.4% and 13.0%.

B. We are 95% confident that the percentage of people who hate broccoli is between 7.4% and 13.0%

C. The margin of error for the true percentage of people who hate broccoli is between 7.4% and 13.0%.

D. All samples of size 1000 will yield a percentage of people who hate broccoli that falls between 7.4% and 13.0%.

E. All of the above.

20. A sample of 31 people was randomly selected from among the workers in a large shoe factory. The time taken for each person to polish a finished shoe was measured. The sample mean was 2.2 minutes. From another study we know that the population standard deviation was 0.72 min. The 90% confidence interval for the true population mean time µ to polish a shoe is

A. (1.98, 2.42)

B. (1.95, 2.45)

C. (1.90, 2.50)

D. (1.99, 2.41)

E. none of the above

21. From a large approximately normal population 30 people are selected at random. If the sample mean age is 85.1 years and the sample standard deviation is 4.5 years, the 95% confidence interval for the true population mean is

A. (83.49, 86.71)

B. (83.46, 86.74)

C. (83.42, 86.78)

D. (83.39, 86.81)

E. none of the above

22. Find, the critical t value for a confidence level of 99% and a sample size of 17.

A. 2.898

B. 2.583

C. 2.921

D. 2.567

E. none of the above

23. The Labor Department wants to estimate the percentage of females in the U.S. labor force. They select a random sample of 525 employment records, and find that 210 of the people are females. The 90% confidence interval is

A. (0.3648, 0.4352)

B. (0.3581, 0.4419)

C. (0.3449, 0.4551)

D. (0.4235, 0.5679)

E. None of the above

24. If the Department of Labor wishes to tighten its interval, they should

A. Increase the confidence level.

B. Increase the sample size.

C. Decrease the sample size.

D. Both A and B

E. Both A and C

25. Statistical inference

A. is reasoning from a sample to a population

B. is reasoning from a population to a sample

C. requires a large sample

D. requires examination of the entire population

E. is based on deductive reasoning.

HW Q:

You must use the proper symbols. In another attachment it is explained how to insert these symbols in a Word document.

Read each problem very carefully and look for the key word or phrase that will tell you how to set up the **Alternative Hypothesis**.

The Null Hypothesis is the opposite of the Alternative Hypothesis.

Then decide if you can use the z or the t-distribution.

For means, use z-distribution if the population standard deviation σ is known, otherwise use the t-distribution.

For proportions we always use the z-distribution.

1. An ambulance service claims that it takes on the average 8.9 min to reach its destination in emergency calls. The agency that licenses ambulance services timed them on 50 random emergency runs, getting a mean of 9.3 min. We know from another study that the population standard deviation = 1.8 min. Is there evidence to support the claim? Use α = 0.05.

**a. State the Null and Alternative Hypotheses:** (Identify which hypothesis is the claim)

**b. Compute the Test statistic: **(Round off correctly)

**c. Find the p-value: **

**d. Make the decision using the Decision Rule. Use the p-value method.**

**e. Write the Conclusion **(in plain English as related to the claim).

2. A large city claims that it provides “free lunch” to more than 30% of its elementary school students. A researcher selects a random sample of 200 students and finds that 72 were getting free lunches. Does the evidence supports the claim at α = 0.05?

**a. State the Null and Alternative Hypotheses: **(Identify which hypothesis is the claim)

**b. Compute the Test statistic: **(Round off correctly)

**c. Find the p-value: **

**d. Make the decision using the Decision Rule. Use the p-value method.**

**e. Write the Conclusion **(in plain English as related to the claim).