Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 13 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.36 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is largeuniform distribution of weightsσ is unknownnormal distribution of weightsσ is known

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.    There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

Suppose a hypertension trial is mounted and 18 participants are randomly assigned to one of the comparison treatments. Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment. The data are as follows.

Is there a difference in mean SBP among treatments? Run the appropriate test at []=0.05.  

Exhibit Symptom of COVID-19

Study shows that about 70% of the COVID-19 patients have a dry cough (which does not bring up any mucus or phlegm). To use hypothesis testing method to check the credibility of this study, you randomly surveyed 25 patients of COVID-19 and 18 of them answered that they are having dry cough.

1. Refer to Exhibit Symptom of COVID-19. What is the value of the test statistics?

2. Refer to Exhibit Symptom of COVID-19. Which of the followings CAN be used to calculate the answer in Question 6? (Select ALL that apply.)

-2*(1 - NORM.DIST( sample proportion, 0.7, std. dev. of population, 1 ))

-2*(1 - NORM.DIST( 18/25, 0.7, sqrt(0.7*0.3/25), 1 ))

-T.DIST.2T( t-test, 24)

-2*T.DIST.RT( (18/25 - 0.7)/(sqrt(0.7*0.3/25)), 24 )

-1 - BINOM.DIST.RANGE(25, 0.7, 25*0.7-0.5, 25*0.7+0.5)

-2*(1 - NORM.DIST( z-test, 0, 1, 1) )

-2*NORM.S.DIST( z-test, 1)

-2*NORM.DIST( 18/25, 0.7, sqrt(0.7*0.3/25), 1 )

-2*(1 - NORM.S.DIST( z-test, 1))

3. In this question, the symbol "<=" means "", and ">=" means "".

Suppose you the significance level you have chosen is α=0.09. This corresponds to a critical value to be  [ Select ] . Hence, you will  [ Select ] the null hypothesis H0. And conclude that, from this sample of 25 patients, there is  [ Select ] to say that the population proportion of dry cough symptom is  [ Select ] . This is because the p-value is  [ Select ] the α value, and the relationship between the test statistic and the critical value is  [ Select ] .

The following data are given for a two-factor ANOVA with two treatments and three blocks.

Block 1 2

A 47 30

B 31 29

C 47 36

Using the 0.05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ.

State the decision rule for treatments. (Round your answer to 1 decimal place.)

State the null and alternate hypotheses for blocks. (Round your answer to 1 decimal place.)

Also, state the decision rule for blocks.

Compute SST, SSB, SS total, and SSE and complete an ANOVA table. (Round your SS, MS values to 3 decimal places and F value to 2 decimal places.)

A summer camp hired 20 counselors for the summer. Ten were male and ten were female. There is a concern that the males were paid more for the summer work than the females. To investigate this concern, males and females were paired based on their experience. Pair Male Female 1

14,300 13,800

2 16,500 16,600

3 15,400 14,800

4 13,500 13,500

5 18,500 17,600

6 12,800 13,000

7 14,500 14,200

8 16,200 15,100

9 13,400 13,200

10 14,200 13,500

Calculate the appropriate t-value testing the hypothesis that male counselors are paid more than female counselors. Give your calculated t-value to two decimal places.

A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course’s completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed here. It is know that the population standard deviation is 8. The instructor has recommended that the students devote 36 hours to the course for the semester. Test to determine at the 1% significance level whether there is evidence that the average student spent less than the recommended amount of time. 31 40 26 30 36 38 29 40 38 30 35 38

The quarterly sales data (number of copies sold) for a college textbook over the past three years follow.

Click on the datafile logo to reference the data.

quarter year 1 year 2 year 3  

1 1690 1800 1850

2 940 900 1100

3 2625 2900 2930

4 2500    2360    2615

e. Deseasonalize the time series (to 3 decimals).

f. Compute the linear trend equation for the deseasonalized data (to 1 decimal if necessary).
Deseasonalized Value =____ +____ Period

Compute the forecast sales using the linear trend equation (to 1 decimal).

g. Adjust the linear trend forecasts using the adjusted seasonal indexes computed in part (c) (to the nearest whole number).

A particular fruit's weights are normally distributed, with a mean of 401 grams and a standard deviation of 40 grams.

If you pick 24 fruit at random, what is the probability that their mean weight will be between 387 grams and 403 grams

A)The life expectancy in the United States has a mean of 75 with a standard deviation of 7 years and follows a normal distribution.

What is the probability of an individual living longer than 80 years?

b)In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465.

What is the probability that UTC will defeat Furman given that they defeat Marshall?

c) In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465.

Are the outcomes of the games independent? Explain and given reasoning for your answer.

What is the probability that UTC will win Furman or Marshall?

A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table.  

   Number of cigarettes smoked per day
0 1-14 15 and over

Wear seat belts 168 30 50

Don't wear seat belts 150 25 77

At the 0.05 significance level, test the claim that the amount of smoking and seat belt use are related. The alternative hypothesis (H_1) is

Select one:

a. p_{0} = p_{1-14} = p_{15 and over} =1/3

b. The amount of smoking is dependent on seat belt use

c. None of the other answers in necessary true.

d. p_{wear seat belts} = p_{don't wear seat belts}

e. The amount of smoking is independent of seat belt use

1. Using the entire data set of 65 stocks, count up the number of stocks in your data that have a high stock price that is at least $20. State this value here: ___28____. (is it)?

Verify this by copying the stem-and-leaf display for the high prices below.

1. Suppose it is desired to determine if the true percentage of all stocks that have high prices that are at least $20 differs from 40%. Is the sample size large enough to conduct this test? Why or why not? Show your calculations for full credit!

2. Use the table on the next page to locate the number of your stocks with high prices of at least $20 in your sample. Use the table to locate the Test Statistic that you should use for this test and write it here:

3. Give the rejection region for this test (you choose an acceptable level for a).

2. In the words of the problem, give a practical conclusion for this test. Make sure to include your choice of α in this conclusion.

1. Shown below is a partial Excel output from a regression analysis.

A.Forty- three percent of Americans use social media and other websites to voice their options about television programs (the Huffington post, November 23, 2011). Below are the results of survey of 1364 individuals who were asked if they use social media and other websites to voice their options about television programs.

   uses social media and other websites to    Doesn't use social media and other websites to voice options about television program

voice options about Television program

Female 395 291

Male 323 355

a.Show a joint probability table.

b.What is the probability a respondent is female?

c.What is the conditional probability a respondent uses social media and other websites to voice options about television programs given the respondent is female?

d.Let F denote the event that the respondent is female and A denote the event that the respondent uses social media and other websites to voice options about television program. Are events F and A independent ?

B. The college board reported the following mean scores for the three parts of the SAT ( The world Almanac, 2009):

Critical reading 502

Mathematics 515

Writing 494

Assume that the population standard deviation on each part of the test is 100.

a.What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the populations mean of 502 on the critical reading part of the test?

b.What is the probability that a random sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the mathematics part of the test ? Complete this Probability to the value computed in part (a).

Is the quotient of two independent geometric random variables a geometric random variable? If not, what is its distribution?

What return on the stock would be expected if S&P 500 Return was -4%?

Give a 95% confidence interval for the coefficient for S&P 500 Returns.

Looking both at the specification of the model and at the estimated coefficient, how can you interpret the coefficient of S&P 500 Returns?