There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations.

Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Use a 1% level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ₁ = μ₂ = μ₃; H₁: Not all the means are equal.H₀: μ₁ = μ₂ = μ₃; H₁: At least two means are equal.     H₀: μ₁ = μ₂ = μ₃; H₁: Exactly two means are equal.H₀: μ₁ = μ₂ = μ₃; H₁: All three means are different.

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Round your answers to three decimal places.)

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Round your answers for MS_BET, and MS_W to two decimal places.)

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


What are the degrees of freedom?

(c) Find the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100     0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value is greater than the level of significance at α = 0.01, we do not reject H₀.Since the P-value is less than or equal to the level of significance at α = 0.01, we reject H₀.     Since the P-value is greater than the level of significance at α = 0.01, we reject H₀.Since the P-value is less than or equal to the level of significance at α = 0.01, we do not reject H₀.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal.     At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal.

(f) Make a summary table for your ANOVA test. (Round your answers for SS to three decimal places, your MS and F Ratio to two decimal places, and your P-value to four decimal places.)

An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 44 and σ = 5.0.

(a) What is the probability that yield strength is at most 40? Greater than 64? (Round your answers to four decimal places.)

(b) What yield strength value separates the strongest 75% from the others? (Round your answer to three decimal places.)
____________ ksi

Consider the following ANOVA experiments. (Round your answers to two decimal places.)

(a) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis H₀: μ₁ = μ₂ = μ₃ = μ₄, with n = 23 and α = 0.01.
F ≥

(b) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅, with n = 16 and α = 0.025.
F ≥

(c) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis H₀: μ₁ = μ₂ = μ₃, with n = 22 and α = 0.01.
F ≥

1. List all possible samples of n=2 from the following population {1,2,3,5,6,7} (note that there is no number 4 in the population). Assume that those numbers represent the years of age of six different people. Create a sampling distribution of the 15 different sample means based on each possible pair (e.g., the sample {2,1} represents on possible such pair). Assume further that the order of the numbers does not matter (e.g., the pair {1,2} is the same as the pair {2,1}). Compute the expected value of the resulting sampling distribution (i.e., the mean age or μ) based on the 15 different sample means. Compute the standard deviation (i.e., the standard error or SE) of the resulting sampling distribution based on the 15 different sample means.

2. Based on the sampling distribution you created in question 2 above, what is the probability of underestimating (i.e., the probability to the left) the true population mean age (μ) by 2 years.

Suppose you roll two ordinary dice. Calculate the expected value of their product. Solve using R studio coding.

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.6 hours and the standard deviation is 2.1 hours. If 36 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.9 hours.

please add explanation and solve

The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/10 where x goes between 1 and 11 minutes. Round answers to 4 decimal places when possible.

A)Find the probability that the time will be at most 7 minutes.

B)Find the probability that the time will be between 4 and 6 minutes.

C)The standard deviation is?

A researcher is interested in knowing whether early childhood education has an impact on graduate earnings. She finds 14 published studies that have tested the null hypothesis that there is no impact. Since the studies were conducted at different times in different countries, it is reasonable to assume that the samples are statistically independent.

Assuming that there is in fact no relationship between early childhood education and graduate earnings, what is the probability that at least one of the 14 studies will reject the null hypothesis at a 10% significance level?

1. Compute the number of passwords of each type below along with how long it would take to test all possible such passwords if it takes 1 nanosecond to test a password. Report the times in the most convenient human understandable form. In all of these, unless noted otherwise, order matters and repetition of characters is allowed.
   1. Passwords of length 8 with any combination of lowercase letters, uppercase letters, and numbers.
   2. Passwords that start with a capital letter, have 10 lowercase letters, and end with a number.
   3. Passwords that start with a capital letter, have between 10 and 20 lowercase letters, and end with a number.
   4. Passwords that have four words in them, where the words come from a list of 20,000 words.
   5. Passwords using the word ‘password’ with different uses of upper case and lower case letters, and also allowing for a substitution of a number for the letters such as ‘96553014’; each letter is uniquely represented by a number, e.g., p can be replaced with 9 but with no other number. Basically, we have 3 choices per letter in ‘password’. No reordering allowed.
   6. Which of these schemes would you use for your bank account?

A vitamin K shot is given to infants soon after birth. Nurses at Northbay Healthcare were involved in a study to see if how they handle the infants could reduce the pain the infants feel ("SOCR data nips," 2013). One of the measurements taken was how long, in seconds, the infant cried after being given the shot. A random sample was taken from the group that was given the shot using conventional methods (first table), and a random sample was taken from the group that was given the shot where the mother held the infant prior to and during the shot (second table).  

Crying Time of Infants Given Shots Using Conventional Methods

Crying Time of Infants Given Shots Using New Methods

You may assume the 2 sample t-procedures are safe to use. Call conventional 1 and new 2 in proceeding with analyses.

#10. Find the 95% confidence interval for the mean difference in mean crying time after being given a vitamin K shot between infants held using conventional methods and infants held by their mothers. Fill in blank 1 to report the bounds of the 95% CI. Enter your answers as lower bound,upper bound with no additional spaces and rounding bounds to three decimals.

Blank #1: 95% confident that the true mean difference in mean crying time after being given a vitamin K shot between infants using conventional methods and infants held by their mothers is between ____________and ___________________. In other words, the mean crying time of infants given vitamin K shot using conventional methods is anywhere from ______________ less than to _______________more than the mean crying time of infants given vitamin K shot using new methods.

#9. Is there enough evidence to show that infants cried less on average when they are held by their mothers than if held using conventional methods? Test at the 5% level.

Use the framework below to guide your work.

Hypotheses: :     Ho: mu1 = mu2; Ha: mu1 > mu2 (calling conventional 1 and new 2)   

Blank #2: Test statistic = _________ (round to two decimal places)

Blank #3:  p-value = __________ (round to four decimal places)

Blank #4: Test decision: We decide to ___________ Ho (reject or do not reject)

Blank #5: Conclusion back into the words of problem: The evidence __________(favors or does not favor) that the mean crying time of infants given vitamin K shot and being held by their mothers is less than the mean crying time of those who were given shot using conventional methods.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 61 professional actors, it was found that 45 were extroverts. (a) Let p represent the proportion of all actors who are extroverts. Find point estimates for p and q. (Round your answer to four decimal places.) p̂ = q̂ = (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) Find the maximal margin of error. (Round your answer to two decimal places.) E = Report the bounds from the 95% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. We are 5% confident that the true proportion of actors who are extroverts falls above this interval. We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. We are 95% confident that the true proportion of actors who are extroverts falls within this interval. We are 5% confident that the true proportion of actors who are extroverts falls within this interval. (c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial.

The research center of a university collects data on employment and hourly earnings in private industry groups. Eighteen people working in the manufacturing industry are selected at random. Their average hourly earnings, in dollars, are as follows.

52.6 45.9 62.0 74.2 80.6 77.5 34.8 46.8 48.4 68.7 41.2 52.5 58.9 66.2 69.9 57.1 63.3 102.9

(a) Construct a frequency distribution and a relative frequency distribution for these hourly earnings. Use a first cutpoint of 34 and classes of equal width 9.

(b) Describe the distribution of hourly earnings.

(c) Obtain the five-number summary.

(d)Are there any outliers? Show appropriate calculations.       

(e) Is a pie chart appropriate for this distribution of hourly earnings? Why or why not?

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .35.

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)? Use 95% confidence.

b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?

1. You are evaluating two contractors for cleaning up Superfund sites. You oversee the cleanup of mining Superfund sites and factory-based Superfund sites. You are interested in selecting the contractor that has most often done the cleanup within the allotted time frame.

Contractor A did 48 mining Superfund sites, finishing 12 of them on time. They also did 572 factory-based sites, finishing 183 on time.

Contractor B has done 412 mining Superfund sites, finishing 105 on time. They also did 140 factory-based sites with 45 of them being finished on time.

1. What is the overall ratio of completing the projects on time for each contractor? Based on this alone, which contractor would you choose?
2. If you had to choose one for a mining site, which one would you choose? Justify.
3. If you had to choose one for a factory site, which one would you choose? Justify.
4. If you had to choose one to handle both sites, which one would you choose? If this contradicts any of your other choices, be sure to comment on resolving the contradiction.

1.

Seams Personal advertises on its website that 95% of customer orders are received within four working days. They performed an audit from a random sample of 500 of the 6,000 orders received that month and it shows 470 orders were received on time.

(Question) If Seams Personal customers really receive 95% of their orders within four working days, what is the probability that the proportion in the random sample of 500 orders is the same as the proportion found in the audit sample or less?

2.

You collect a random sample of size n from a population and calculate a 98% confidence interval. Which of the following strategies produces a new confidence interval with a decreased margin of error?

Use a 99% confidence level.  Use a 95% confidence level.  Decrease the sample size.  Use the same confidence level, but compute the interval n times. Approximately 2% of these intervals will be larger.  Nothing can guarantee that you will obtain a larger margin of error. You can only say that the chance of obtaining a larger interval is 0.02.

3.

Faculty members at Lowell Place High School want to determine whether there are enough students to have a Valentine's Day Formal. Eighty-eight of the 200 students said they would attend the Valentine's Day Formal. Construct and interpret a 90% confidence interval for p.

The 90% confidence interval is (0.4977, 0.5023). We are 90% confident that the true proportion of students attending the Valentine's Day Formal is between 49.77% and 50.23%.  The 90% confidence interval is (0.3823, 0.4977). There is a 90% chance that a randomly selected student who will attend the Valentine's Day Formal lies between 38.23% and 49.77%. The 90% confidence interval is (0.4977, 0.5023). Ninety percent of all samples of this size will yield a confidence interval of (0.4977, 0.5023). The 90% confidence interval is (0.3823, 0.4977). Ninety percent of all samples of this size will yield a confidence interval of (0.3823, 0.4977). The 90% confidence interval is (0.3823, 0.4977). We are 90% confident that the true proportion of students attending the Valentine's Day Formal is between 38.23% and 49.77%.