In a simple random sample of 1000 people age 20 and over in a certain​ country, the proportion with a certain disease was found to be 0.160 ​(or 16.0​%). Complete parts​ (a) through​ (d) below.

A. What is the standard error of the estimate of the proportion of all people in the country age 20 and over with the​ disease?

B. Find the margin of​ error, using a​ 95% confidence​ level, for estimating this proportion.

C. Report the​ 95% confidence interval for the proportion of all people in the country age 20 and over with the disease. m=___

The​ 95% confidence interval for the proportion is (_,_)

D. According to a government​ agency, nationally, 17.1​% of all people in the country age 20 or over have the disease. Does the confidence interval you found in part​ (c) support or refute this​ claim? Explain.

The confidence interval (refutes OR supports) this​ claim, since the value _ (is OR is not) contained within the interval for the proportion.

A television station wishes to study the relationship between viewership of its 11 p.m. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 p.m. news is found for each sample. The results are given in the table below.

		Age Group
Watch 11 p.m. News?	18 or less	19 to 35	36 to 54	55 or Older	Total
Yes	42	57	61	82	242
No	208	193	189	168	758
Total	250	250	250	250	1,000

(a) Let p₁, p₂, p₃, and p₄ be the proportions of all viewers in each age group who watch the station’s 11 p.m. news. If these proportions are equal, then whether a viewer watches the station’s 11 p.m. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H₀ that p₁, p₂, p₃, and p₄ are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05. (Round your answer to 3 decimal places.)

χ2χ2 =            

so (Click to select)Do not rejectReject H₀: independence

(b) Compute a 95 percent confidence interval for the difference between p₁ and p₄. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

95% CI: [  , ]

A researcher is interested in investigating whether religious affiliation and the brand of sneakers that people wear are associated. The table below shows the results of a survey.

Frequencies of Religions and Sneakers

	Nike	Adidas	Other
Protestant	97	100	101
Catholic	54	61	100
Jewish	15	25	24
Other	85	61	73

What can be concluded at the αα = 0.10 significance level?

What is the correct statistical test to use?

Independence

Paired t-test

Homogeneity

Goodness-of-Fit

What are the null and alternative hypotheses?
H0:H0:

The distribution of sneaker brand is not the same for each religion.

Sneaker brand and religious affiliation are independent.

Sneaker brand and religious affiliation are dependent.

The distribution of sneaker brand is the same for each religion.

H1:H1:

The distribution of sneaker brand is the same for each religion.

The distribution of sneaker brand is not the same for each religion.

Sneaker brand and religious affiliation are dependent.

Sneaker brand and religious affiliation are independent.

The test-statistic for this data =  (Please show your answer to 2 decimal places.)

The p-value for this sample = (Please show your answer to 4 decimal places.)  

The p-value is Select an answer greater than less than (or equal to)  αα  

Based on this, we should

fail to reject the null

reject the null

accept the null

Thus, the final conclusion is...

There is sufficient evidence to conclude that the distribution of sneaker brand is not the same for each religion.

There is insufficient evidence to conclude that the distribution of sneaker brand is not the same for each religion.

There is sufficient evidence to conclude that sneaker brand and religious affiliation are dependent.

There is sufficient evidence to conclude that sneaker brand and religious affiliation are independent.

There is insufficient evidence to conclude that sneaker brand and religious affiliation are dependent.

2. A standard 52-card deck consists of 4 suits (hearts, diamonds, clubs, and spades). Each suit has 13 cards: 10 are pip cards (numbered 1, or ace, 2 through 10) and 3 are face cards (jack, queen, and king).

You randomly draw a card then place it back. If it is a pip card, you keep the deck as is. If it is a face card, you eliminate all the pip cards. Then, you draw a new card. What is the probability you draw the queen of hearts in the end?

A new battery’s voltage may be acceptable (A) or unaccept- able (U). A certain flashlight requires two batteries, so bat- teries will be independently selected and tested until two acceptable ones have been found. Suppose that 90% of all batteries have acceptable voltages. Let Y denote the number of batteries that must be tested.

a) What is p(2), that is, P(Y 5 2)?

b) What is p(3)? [Hint: There are two different outcomes

that result in Y 5 3.]

c) To have Y 5 5, what must be true of the fifth battery

selected? List the four outcomes for which Y 5 5 and

then determine p(5).

d) Use the pattern in your answers for parts (a)–(c) to obtain

a general formula for p(y)

e) instead of the random variable Y given in the textbook, define a Negative Binomial random variable and do this question. Also, state the mean and standard deviation for this negative binomial random variable and interpret it in the context of the question

(4 pts.) Couples' therapists performed a study to determine factors that would predict divorce. A random sample of 180 committed couples produced a sample mean of the time that they knew each other of 52.28 months. Assume a population standard deviation of 41.40 months. Construct a 95% confidence interval for the mean time that spouses have known each other among all married couples.

Customers enter the camera department of a store at an average rate of five per hour. The department is staffed by one employee, who takes an average of 8.0 minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. (Use the Excel spreadsheet Queue Models.)

a-1. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? (Round your answer to 2 decimal places.)

a-2. How long would a customer expect to spend in the camera department (total time)? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

b. What is the utilization of the clerk? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

c. What is the probability that there are more than two people in the camera department (excluding the clerk)?(Do not round intermediate calculations. Round your answer to 1 decimal place.)

d. Another clerk has been hired for the camera department who also takes an average of 8.0 minutes to serve each arrival. How long would a customer expect to spend in the department now? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

Two dice are tossed one after the other. What is the conditional probability that the first die is six, given that the sum of the dice is seven?

Your company is considering two products for a new market. The probability distribution for the demand for the two products is presented in the table below. Q(A) and Q(B) are the possible quantities of each product that could be sold. P(A) and P(B) are the probabilities of selling the corresponding quantities.

Q(A)	P(A)	Q(B)	P(B)
10000	0.15	10000	0.25
30000	0.20	30000	0.30
50000	0.40	50000	0.35
60000	0.25	60000	0.15

You have the following additional information: The projected selling price for DESIGN "A" is $60. The fixed cost of its production is$75,000. Its variable cost is $35 a unit. The selling price for DESIGN "B" is $80. Its fixed cost of production is $110,000. Variable cost of production is $48 a unit.

Which project is expected to be more profitable?

The customer expectation when phoning a customer service line is that the average amount of time from completion of dialing until they hear the message indicating the time in queue is equal to 55.0 seconds (less than a minute was the response from customers surveyed, so the standard was established at 10% less than a minute).  

You decide to randomly sample at 20 times from 11:30am until 9:30pm on 2 days to determine what the actual average is.  The actual data was as follows:

54.1, 53.3, 56.1, 55.7, 54.0, 54.1, 54.5, 57.1, 55.2, 53.8,54.1, 54.1, 56.1, 55.0, 55.9, 56.0 ,54.9, 54.3, 53.9, 55.0

What is a 95% confidence interval for the true mean call completion time?

What is the 95% confidence interval on the standard deviation

The customer expectation when phoning a customer service line is that the average amount of time from completion of dialing until they hear the message indicating the time in queue is equal to 55.0 seconds (less than a minute was the response from customers surveyed, so the standard was established at 10% less than a minute).  

You decide to randomly sample at 20 times from 11:30am until 9:30pm on 2 days to determine what the actual average is.  The actual data was as follows:

54.1, 53.3, 56.1, 55.7, 54.0, 54.1, 54.5, 57.1, 55.2, 53.8,54.1, 54.1, 56.1, 55.0, 55.9, 56.0 ,54.9, 54.3, 53.9, 55.0

What is a 95% confidence interval for the true mean call completion time?

What is the 95% confidence interval on the standard deviation

hours studied	X^2	score on quiz	Y^2	XY
1	1	3	9	3
2	4	5	25	10
3	9	7	49	21
5	25	9	81	45

sigmaX=11 sigmaX^2=39 sigmaY=24    sigmaY^2=164 sigmaXY=79

part a:

1.what is the predictor variable?

2. what is the criterion variable?

compute the Pearson correlation.

3. what is the covariance.

4 what is the standard deviation of the predictor variable.

5 what is the standard deviation of the criterion variable.

6 what is the Pearson's r value

7. what is the best interpretation of your Pearson correlation in Q6? A. as hours studied goes up there is a corresponding increase in score on quiz. B. As hours studied goes up there is a corresponding decrease in score on quiz.

8. The strength of the above relationship is considered.    A, weak b. moderate    c. strong.

Part B. compute the regression equation.

9. what is the numeric value for the slope?

10. what is the y-intercept?

11. what is the regression equation?

12. predict the total number of points on the quiz for a person studying 4 hours.

You took independent random samples of 20 students at City College and 25 students at SF State. You asked each student how many sodas they drank over the course of a year. The sample mean at City College was 80 and the sample standard deviation was 10. At State the sample mean was 90 and the sample standard deviation was 15. Use a subscript of c for City College and a subscript of s for State.

1. Calculate a point estimate of the difference between the two population means.

2. Calculate the appropriate number of degrees of freedom to use for your analysis. Hint: Remember that you always round down for degrees of freedom if you get a decimal answer. Note: To calculate this answer you must use the formula which assumes unequal variances.

3. Determine a 95% confidence interval for the difference between the two population means.

4. Give the null and alternative hypotheses for a hypothesis test to test to see if there is a statistically significant difference in the population means between students at the two schools.

5. State α using the confidence level in question 3.

6. Calculate the value of the test statistic.

7. Find a range for the p-value.

8. What is your conclusion in statistical terms?

9. Explain the meaning of this conclusion in business terms.

10. What statistical conclusion would you reach using the confidence interval approach? Explain how you reach this conclusion. Is it the same conclusion you reached using the p-value approach?

Chi-Square Analysis Worksheet MTH 160: Statistics

Suppose the local state university wants to determine whether there is a relationship between a student’s gender and a student’s major in college. The registrar was asked to randomly select 55 students and record their gender and major. The majors were grouped into categories of Natural Science (NS), Social Sciences (SS), and Humanities (H). Answer the following questions based on the results in the table below.

NS SS H Total

Men 11 9 3 23

Wom 9 13 10 32

Total 20 22 13 55

Part I: 1. Determine the expected frequency for each of the cells within the table.

2. Compute the sample chi-square statistic from the contingency table. 3. Conduct a chi-square test of independence to determine whether there is a relationship between gender and college majors. Show all of your work to support your chi-square test. 4. What conclusion can be determined from the results of the chi-square test? Part II:

Suppose we are only interested in the college majors of the women in our study. We would like to compare our sample to the national percentage of women majoring in each of the categories (NS, SS, and H) and determine whether the sample distribution fits the national distribution. Suppose the national percentage of women majoring in Natural Sciences is 22%, majoring in Social Sciences is 28%, and majoring in the Humanities is 30%.

NS SS H Total

Women 9 13 10 32

1.Conduct a chi-square goodness-of-fit test to determine whether our sample data fits the national distribution. Show all of your work to support your chi-square test.

2. What conclusion can be determined from the results of the chi-square test?

Data

Month	Chevy Cruze	Ford Focus	Hyundai Elantra	Honda Civic	Toyota Corolla	VW Jetta
January	21,711	21,303	21,006	19,341	20,985	19,671
February	18,274	19,385	19,992	20,872	19,785	19,105
March	17,934	16,557	15,713	17,181	16,889	16,006
April	19,387	17,420	15,054	14,500	14,093	14,083
May	17,097	16,147	15,023	15,800	15,727	16,875
June	16,244	16,173	14,295	15,058	15,236	16,893

Phase 1 report must include the preliminary findings:

1. What are the means, medians, modes, range and standard deviation for each of the six car models? Draw box plots.
2. What are the means, medians, modes, range and standard deviations for each of the six months (May – October)? Draw box plots.

Explain the contribution of the Milan Group to family therapy theory.