The sample mean is 19.0, the sample standard deviation is 6.6, and n = 41. Establish a 90% confidence interval for the population mean. (by default two tailed test, α is reliability factor)

6) An economist is interested in studying the average income of consumers in a particular country. The population standard deviation of incomes is known to be $1,000.

What type of confidence interval should the economist build?

Group of answer choices

A t-based interval for the population mean.

No answer text provided.

A Z-based interval for the population proportion.

A Z-based interval for the population mean.

7) A race car driver tested his car for the time it takes to go from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. These times are known to be normally distributed.

What is the value of t used to construct a 95% confidence interval for the mean time it takes the car to go from 0 to 60? Round your answer to 2 decimal places.

8) A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12 feet.A sample of 70 cut sheets yields a mean length of 12.14 feet and a sample standard deviation of 0.15 feet.

What type of confidence interval should the engineer build?

Group of answer choices

A Z-based interval for the population proportion.

A Z-based interval for the population mean.

A t-based interval for the population mean.

Use the following information for Questions 8, 9, and 10

Soda bottles are filled so that they contain an average of 330 ml of soda in each bottle. Suppose that the amount of soda in a bottle is normally distributed with a standard deviation of 4 ml.

8) What is the probability that a randomly selected bottle will have less than 325 ml of soda?  Round your answer to 4 decimal places.

9) What is the probability that a randomly selected six-pack of soda will have a mean less than 325 ml of soda?  Round your answer to 4 decimal places.

10) What is the probability that a randomly selected twelve-pack of soda will have a mean less than 325 ml of soda?  Round your answer to 4 decimal places.

In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30-34 group while Mary competed in the Women, Ages 25-29 group. Leo completed the race in 1:22:28 (4948 seconds) , while Mary completed the race in 1:31:53 (5513 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performance of their groups:

• The finishing times of the Men, Ages 30-34 group have a mean of 4313 seconds with a standard deviation of 583 seconds.
• The finishing times of the Women, Ages 25-29 group have a mean of 5261 seconds with a standard deviation of 807 seconds.
• The distributions of finishing times for both groups are approximately Normal.

Remember, a better performance corresponds to a faster finish.

1. Find the Z-scores for Leo’s and Mary’s finishing times. Did Leo or Mary rank better in their respective groups? Explain your reasoning?
   
   

2. What percent of the triathletes did Leo finish faster than in his group?
   
   
   
3. What percent of the triathletes did Mary finish faster than in her age group?
   

4. What is the cutoff time for the fastest 5% of athletes in the men’s group?

5. What is the cutoff time for the slowest 10% of athletes in the women’s group?
   
   

A company has sales of automobiles in the past three years as given in the table below. Using trend and seasonal components, predict the sales for each quarter of year 4.

identify (but don’t collect) a type of dataset that might vary significantly from its mean. (Examples may be adult’s weights or BMIs, a company’s sales, or the number of pieces of mail you receive in a week. Using your imaginary dataset, answer the following questions:

• What is a brief description of the data?
• How much would you expect the data to vary?
• What might the causes of the variation be?

you are an analyst working for the new Joint High Speed Vessel (JHSV) program office. Several tests have been conducted on two different types of experimental test vessels (denoted simply “1” and “2”) to determine their performance characteristics under various loading and sea state conditions.

With detailed data on the fuel consumption of vessel "1," and with the Navy's new focus on energy efficiency, the program manager wants to test whether the vessel beats the design specs in terms of mean hourly fuel consumption. You decide to conduct a large sample hypothesis test of the data with the goal of conclusively demonstrating, if possible, that the data support the claim that the mean hourly fuel consumption is less than 50 gph (gallons per hour) at 35 knots. Given that for 36 (independent) hours of operation at 35 kts you observe y-bar 49.5 gph with s=2 gph, and using a significance level of a=0.05:

a. Write out the null and alternative hypotheses.

b. Calculate the test statistic.

c. Calculate and state the rejection region or p-value.

d. Conduct the test and state the outcome. State the outcome both in terms of accepting or rejecting the null hypothesis and then in terms of what the result means in the context of this particular problem.

A friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.; 40% of the time she travels on airline #1, 20% of the time on airline #2, and the remaining 40% of the time on airline #3. For airline #1, flights are late into D.C. 40% of the time and late into L.A. 15% of the time. For airline #2, these percentages are 30% and 15%, whereas for airline #3 the percentages are 35% and 20%. If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are the posterior probabilities of having flown on airlines #1, #2, and #3? Assume that the chance of a late arrival in L.A. is unaffected by what happens on the flight to D.C. [Hint: From the tip of each first-generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late, 1 late, and 2 late.] (Round your answers to four decimal places.)

Appropriate sampling is a critical component in developing a good research project. Using your approved research questions and research topic, explain your anticipated sampling method and why this is appropriate for your research proposal. What is your sample size? Next, read and review two of your classmates’ posts and analyze their sampling approach. Are their sampling approaches appropriate? Why or why not?

The number of floods that occur in a certain region over a given year is a random variable having a Poisson distribution with mean 2, independently from one year to the other. Moreover, the time period (in days) during which the ground is flooded, at the time of an arbitrary flood, is an exponential random variable with mean 5. We assume that the durations of the floods are independent. Using the central limit theorem, calculate (approximately)
(a) the probability that over the course of the next 50 years, there will be at least 80 floods in this region. Assume that we do not need to apply half-unit correction for this question.

(b) the probability that the total time during which the ground will be flooded over the course of the next 50 floods will be smaller than 200 days.

A Theater has n numbered seats, and n tickets are distributed among n persons. Compute the probability that

(a) exactly two persons will be seated at seats corresponding to their ticket numbers if all the seats are occupied at random.

(b) at least two persons will be seated at seats corresponding to their ticket numbers if all the seats are occupied at random.

A turfgrass scientist is looking for an optimal approach to control a certain plant disease in Kentucky blue grass. He compares three different management strategies designed so that they would reduce spread of the disease. He has set up a field study with a total of 20 experimental plots and 4 treatments (3 disease prevention treatments and a control treatment. Each treatment has been assigned to 5 randomly selected experimental plots. Plant biomass is then measured from each pot at the end of the experiment. ANOVA table and the treatment means are shown below.

ANOVA:

a) Do all pairwise comparisons between the treatment means using LSD, (a=0.05). Present the results using letters assigned to treatment means (Put the letters in the column Letters for part a) in the above table)

b) Do all pairwise comparisons between the treatment means using Tukey’s HSD (a=0.05). Present the results using letters assigned to treatment means. (Put the letters in the column Letters for part b) in the above table)

c) Comment on differences in conclusions obtained using the two methods. Which method would you use for this analysis? For full credit, provide an explanation of your choice.

Let X be a random variable with CDF F(x) = e^-e(µ-x)/β, where β > 0 and -∞ < µ, x < ∞.

1. What is the median of X?

2. Obtain the PDF of X. Use R to plot, in the range -10<x<30, the pdf for µ = 2, β = 5.

3. Draw a random sample of size 1000 from f(x) for µ = 2, β = 5 and draw a histogram of the values in the random sample drawn. Compare this histogram with the answer in 2 above.

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

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,053. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

(a)

A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of

H0

will support the researcher's contention.

H0: μ > $1,053
Ha: μ ≤ $1,053H0: μ = $1,053
Ha: μ ≠ $1,053    H0: μ ≥ $1,053
Ha: μ < $1,053H0: μ < $1,053
Ha: μ ≥ $1,053H0: μ ≤ $1,053
Ha: μ > $1,053

(b)

For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of

σ = $1,600

may be assumed.

What is the test statistic? (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

(c)

At

α = 0.05,

what is your conclusion?

Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,053.Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,053.    Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,053.Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,053.

(d)

Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses.

H0: μ > $1,053
Ha: μ ≤ $1,053H0: μ = $1,053
Ha: μ ≠ $1,053    H0: μ ≥ $1,053
Ha: μ < $1,053H0: μ < $1,053
Ha: μ ≥ $1,053H0: μ ≤ $1,053
Ha: μ > $1,053

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

State the critical values for the rejection rule. (Use α = 0.05. Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,053.Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,053.    Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,053.Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,053.