You may need to use the appropriate technology to answer this question.

Test the following hypotheses by using the

χ²

goodness of fit test.

A sample of size 200 yielded 80 in category A, 20 in category B, and 100 in category C. Use α = 0.01 and test to see whether the proportions are as stated in

H₀.

(a)

Use the p-value approach.

Find the value of the test statistic.

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.     Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.

(b)

Repeat the test using the critical value approach.

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.)

test statistic ≤test statistic ≥

State your conclusion.

Do not reject H₀. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20.Do not reject H₀. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20.     Reject H₀. We conclude that the proportions are equal to 0.40, 0.40, and 0.20.Reject H₀. We conclude that the proportions differ from 0.40, 0.40, and 0.20.

The college bookstore tells prospective students that the average cost of its textbooks is $108 with a standard deviation of $4.50. A group of smart statistics students thinks that the average cost is higher. In order to test the bookstore’s claim against their alternative, the students will select a random sample of size 100. Assume that the mean from their random sample is $112.80.

1. Perform a hypothesis test (using R) at the 5% level of significance and state your decision. Also construct a 90% confidence interval (using R) for the average cost of textbook.
2. Perform the above task under the assumption that the students selected a random sample of size 10.
3. Write the difference between your findings of (1) and (2).

1. A clinician claims that, on average, the blood pressure of hypertensive patients is 150. A particular doctor believes the amount is more than 150. Then he selected a random sample of 100 patients and found that the sample have average of 155 with standard deviation of 10. Conduct the test at the 0.05 of significance. a) Hypotheses HO: vs. HA a) Test statistic b) P-value c) Conclusion d) What is the power of the test conditions to identify a significant difference if the population mean was actually 152 at α=0.05 (two sided)? e) How large a sample is needed for a one-sample z test with 80% power and α = 0.05 (two-tailed) when σ = 10?

You may need to use the appropriate technology to answer this question.

A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: the company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows.

(a)

Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company.

State the null and alternative hypotheses.

H₀: Employment plan is mutually exclusive from the type of company.
H_a: Employment plan is not mutually exclusive from the type of company.H₀: Employment plan is not independent of the type of company.
H_a: Employment plan is independent of the type of company.     H₀: Employment plan is not mutually exclusive from the type of company.
H_a: Employment plan is mutually exclusive from the type of company.H₀: Employment plan is independent of the type of company.
H_a: Employment plan is not independent of the type of company.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

At a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We cannot conclude that the employment plan and the type of company are not independent.Reject H₀. We conclude that the employment plan is not independent of the type of company.     Reject H₀. We conclude that the employment plan is independent of the type of company.Do not reject H₀. We cannot conclude that the employment plan and the type of company are independent.

(b)

Discuss any differences in the employment plans for private and public companies over the next 12 months. (Round your numeric answers to two decimal places.)

Employment opportunities look to be much better for public companies, while private companies have the greater proportions of "no change" and "lay off employees" planned.Employment opportunities look to be much better for private companies, while public companies have the greater proportions of "no change" and "lay off employees" planned.     Employment opportunities look to be about the same for both public and private companies, with high proportions of "no change" and "lay off employees" planned for both.Employment opportunities look to be about the same for both public and private companies, with high proportions of "add employees" planned for both.

Assume that 15% of circuit boards used in manufacturing compact displayers are defective. Off a batch of 200 randomly selected such circuit boards, use the normal approximation with the continuity correction to find the probability that at most 30 of these boards are defective. Is your answer approximate or exact.

b. find exact probability using R code to compare answer on the previous question?

Please do in Excel

A bank with a branch located in a commercial district of a city has the business objective of improving the process for serving customers during the noon-to-1 p.m. lunch period. To do so, the waiting time (defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected and the waiting times are collected and stored in Bank1 . These data are:

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20

4.50 6.10 0.38 5.12 6.46 6.19 3.79

Suppose that another branch, located in a residential area, is also concerned with the noon-to-1 p.m. lunch period. A random sample of 15 customers is selected and the waiting times are collected and stored in Bank2 . These data are:

9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35

10.49 6.68 5.64 4.08 6.17 9.91 5.47

a. Is there evidence of a difference in the variability of the waiting time between the two branches? (Use a = 0.05.)

b. Determine the p-value in (a) and interpret its meaning.

c. What assumption about the population distribution of each bank is necessary in (a)? Is the assumption valid for these data?

d. Based on the results of (a), is it appropriate to use the pooled-variance t test to compare the means of the two branches?

The Reviews editor for a certain scientific journal decides whether the review for any particular book should be short (1–2 pages), medium (3–4 pages), or long (5–6 pages). Data on recent reviews indicates that 60% of them are short, 30% are medium, and the other 10% are long. Reviews are submitted in either Word or LaTeX. For short reviews, 80% are in Word, whereas 40% of medium reviews are in Word and 30% of long reviews are in Word. Suppose a recent review is randomly selected.

a)What is the probability that the selected review was submitted in Word format?

b)If the selected review was submitted in Word format, what are the posterior probabilities of it being short, medium, or long? (Round your answers to three decimal places.)

Confidence Intervals for Means

Complete each of the following calculations by providing the correct formula and values that you are using for each problem.

1) A sample size of n = 120 produced the sample mean of ? ̅ = 24.3. Assuming the population standard deviation ? = 5.2, compute a 99% confidence interval for the population mean. Interpret the confidence interval.


2) Assuming the population standard deviation ? = 4, how large should a sample be to estimate a population mean with a margin of error of 0.2 for a 95% confidence interval?


3) The manager of a plant would like to estimate the mean amount of time a worker takes to complete a specific task. Assume the population standard deviation for this task is 4.1 minutes.

a. After observing 70 workers completing the same type of task, the manager calculated the average time to be 12.7 minutes. Construct a 90% confidence interval for the mean task time. Interpret the confidence interval.

b. How large a sample size n should he observe to decrease the margin of error to 0.5 minutes for the 90% interval?

4) A sample of 25 was selected out of a specific population with mean equal to 18.4 and sample standard deviation of 3.6. Construct a 95% confidence interval for the mean of the population. Interpret the confidence interval.


5) A group of students were randomly selected to participate in a study that compared the female grades to the male grades for a specific test. There were 15 females with a mean grade of 94.3 and sample standard deviation of 3.6. There were 12 males with a mean grade of 90.6 and sample standard deviation of 5.1. Construct a 90% confidence interval for the difference between the females’ and males’ test grades. Interpret the confidence interval.

Use the following scenario and data to answer questions 12.1 – 12.5. A researcher is interested in how many days it takes athletes to recover from jet lag when they have had to fly a long distance. It is commonly known that traveling east (moving “ahead” in time) leads to more serious jet lag than travelling west. The researcher finds 18 professional athletes who just travelled a long distance; six stayed in the same time zone, six travelled west, and six travelled east.

12.1 Calculate the sum of squares for each treatment condition (SHOW WORK)

SS_w =                                         SS_e =                                          SS_s =

12.2 What is the value of N in this experiment?

12.3 What number should appear in the denominator of your F-ratio? (I want the actual number, not the name of it)

12.4 What number should appear in the numerator of your F-ratio? (I want the actual number, not the name of it) (SHOW WORK)

12.5 Do the data show a significant difference in jet lag depending on the direction of travel? Use a two-tailed test and alpha = .05.

What are the two hypotheses of the F test?

In order for the F test to be significant, do you need a high or a low value of R2? Why? How are the standardized regression coefficients computed?

How are they useful?

What are their measurement units?

Please provide several examples of a negative correlation coefficient.

Explain why the results of a presidential election poll can sometimes lead to an inaccurate conclusion about who will win the election. Hint: Chapter 6 should help you understand this.

9. Police plan to enforce speed limits by using radar traps at four different locations within the city limits. A person who is speeding on his/her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations (location 1, location 2, location 3, and location 4, respectively). The radar traps at each of the locations (location 1, location 2, location 3, and location 4, respectively) will be operated 40%, 30%, 20%, and 30% of the time. If a randomly selected person received a speeding ticket on his/her way to work, what is the probability that he/she passed through the radar trap located at location 1? (10 points)

Hint: Consider the following five events:

A: a speeding person receives a speeding ticket (note: a speeding person will receive a speeding ticket if the person passes through the radar trap when operated.)

B₁: a speeding person passing through location 1,

B₂: a speeding person passing through location 2,

B₃: a speeding person passing through location 3,

B₄: a speeding person passing through location 4.

A deck consists of 72 cards with 9 suits labelled ? to ? and numbered ranks from 1 to 8. That is, there are 8 cards of each suit and 9 cards of each rank. What is the probability of it being suit C or having rank 6?

Use the following information for Questions 1-3: At Regan's Tomato Heaven Farm, the yield per acre, measured in bushels of tomatoes, is known to follow a Normal Distribution with variance σ2 = 225.

1. A random sample is obtained with the following results:

n=16.

Sample mean X-Bar: 56.

Provide a test of null hypothesis H0: μ = 48 versus the alternative hypothesis HA: μ ≠ 48 with α = 0.05.

a. Calculated Z-Score =

b. Z-Critical =

c. Conclusion (Reject H0/Fail to Reject H0)

3. Another random sample is obtained with the following results:

n=36.

Regan would like to conduct a test of null hypothesis H0: μ = 55 versus the alternative hypothesis HA: μ < 55 with α = 0.01

a. Z-Critical =

b. X-Bar Critical. That is, at what value of X-Bar woud you reject H0: