Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at an archaeological site. At one excavation, a sample of 173 potsherds indicated that 64 were of the three-circle, red-on-white pattern.

(a) Find a point estimate p̂ for the proportion of all ceramic potsherds at this site that are of the three-circle, red-on-white pattern. (Round your answer to four decimal places.)

= 0.3699

(b) Compute a 95% confidence interval for the population proportion p of all ceramic potsherds with this distinctive pattern found at the site. (Round your answers to three decimal places.)

Lower Limit =

Upper Limit =

A researcher wishes to investigate the idea that eating sea salt raises blood pressure less than eating normal table salt. He randomly selects two groups, each with 13 people. He arranges that Group 1 will be on a high sea salt diet for 2 weeks, while Group 2 will be on a high table salt diet. He measures their blood pressure after the two weeks. The mean systolic blood pressure for Group 1, x¯1x¯1, is found to be 126 with a sample standard deviation of 4.0, while for Group 2 the mean, x¯2x¯2 is found to be 116 with a sample standard deviation of 3.7. Suppose the null hypothesis is that x¯1=x¯2x¯1=x¯2. Calculate the appropriate statistic to investigate whether the null hypothesis is likely to be valid.

In each of the following exercises, formulate an appropriate null hypothesis and perform a test of that null hypothesis at the 5% and 1% significance levels. Use a one-sided or two-sided test as appropriate.

10. An instructor administers a 2-minute sit-up test to a class of 10 students, obtaining the following scores.
X : 55,45,48,62,58,60,42,44,53,55
The instructor expects students to have an average score of no more than 45 on the sit-up test. Part (a) Assume that 10 is the standard deviation of the sit-up test scores of all the coach’s past and present players.

Please give me step by step answer how to solve this question:

Consider the following example. In a study reported in the California Journal of Nursing, nurses were asked to report their degree of job-related stress. They were asked 20 questions about their work and they responded on a 1-5 scale as the amount of stress they felt (5 being the most). These responses were added up in order to come up with a numeric measure of job stress. Below is the Table with 2 of the groups' data: LVN and RN. Consider the following example. In a study reported in the California Journal of Nursing, nurses were asked to report their degree of job-related stress. They were asked 20 questions about their work and they responded on a 1-5 scale as the amount of stress they felt (5 being the most). These responses were added up in order to come up with a numeric measure of job stress. Below is the Table with 2 of the groups' data: LVN and RN. What do you make of this?

Two random samples of 40 students were drawn independently from two populations of students. Assume their aptitude tests are normally distributed (total points = 100). The following statistics regarding their scores in an aptitude test were obtained: xbar1= 76, s1 = 8, xbar2 = 72, and s2 = 6.5.
Test at the 5% significance level to determine whether we can infer that the two population means differ. (Note: You cannot necessarily assume that the populations have the same variances).

Please Solve manually.

Central Tendency and Variation Activity

1. Roll 4 dice 40 times, recording the sum for each roll.   Do it again so you have two groups of 40 numbers

2. Calculate the mean, median, mode, and midrange for both sets of data. The four numbers should be close to one another for each data set. Write a sentence or two accounting for any discrepancies.

3. Calculate a 5 number summary for both sets of data (it may help to create a tally chart or stem and leaf plot for both sets of data. Write a sentence or two describing any differences between the two sets of number and offer reasons for the discrepancy.

4. Calculate the standard deviation for both sets of data. Which data set is more spread out? Why is this so?       

A hypothesis test is to be performed with a Null hypothesis H_o: µ ≤ 20 and an alternative hypothesis H₁: µ > 20,  the population standard deviation is σ=3.0, the sample size is; n=30, and the significance level is α=0.025.

1) what is a type l error?

a. reject h0 when h0 is incorrect

b. reject h0 when h0 is correct

c. do not reject h0 when h0 is incorrect

d. do not reject h0 when h0 is correct

2) What is the chance of making a type I error in the above test?

a. 0.050

b. 0.0250

c. 0.0125

d. 0.1000

3. What is a type ll error?

a. reject h0 when h0 is incorrect

b. reject h0 when h0 is correct

c. do not reject h0 when h0 is incorrect

d. do not reject h0 when h0 is correct

4.  What value would the sample mean have to be greater than to reject Ho? (answer must be 3dp)

5.  It is unknown to the technician making the test, but the real value of µ=22.
What is the probability that a Type II error occurs?

6. In a word what will happen to the Type II error if the sample size increases to 60 and all else remains unchanged. Including the answer to question (4)

a. increase

b. decrease

The following table reports prices and usage quantities for two items in 2009 and 2011. (Round your answers to the nearest integer.)

(a)Compute price relatives for each item in 2011 using 2009 as the base period.

(b) Compute an unweighted aggregate price index for the two items in 2011 using 2009 as the base period.

I₂₀₁₁ = ___________.

(c) Compute a weighted aggregate price index for the two items using the Laspeyres method using 2009 as the base period.

I₂₀₁₁ = ___________.

(d) Compute a weighted aggregate price index for the two items using the Paasche method using 2009 as the base period.

I₂₀₁₁ = ____________.

A certain beverage company provides a complete line of beer, wine, and soft drink products for distribution through retail outlets in central Iowa. Unit price data for 2011 and 2014 and quantities sold in cases for 2011 follow. Use 2011 as the base period.

Compute the price relatives for this company's products. (Round your answers to two decimal places.)

Use a weighted average of price relatives to show that this method provides the same index as the weighted aggregate method. (Round your answers to the nearest integer.)

weighted average of price relatives index=_______.

weighted aggregate price index=________.

The National Football League (NFL) holds its annual draft of the nation's best college football players in April each year. Prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are selected earlier in the draft. Suppose the following table shows projections by one mock draft service of what position in the first round players from the Atlantic Coast Conference, the Big Ten Conference, the PAC-12 Conference, and the Southeastern Conference will be selected.

Use the Kruskal-Wallis test to determine if there is any difference among NFL teams for players from these four conferences. Use α = 0.05.

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

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

p-value =__________.

9. At a certain school, 41% of the students play soccer, 30% play volleyball, and 14% play both soccer and volleyball. If a student is chosen at random, find the probability that he/she plays neither soccer nor volleyball.: *
(A) 0.71
(B) 0.57
(C) 0.43
(D) 0.413

Questions 10-12: A simple linear regression model was fit to the situation of using the number of pages in a book (in hundreds) to predict the number of typos in the book. The equation is y = 1.2 + 3.4x.

10. Interpret the slope.: *
(A) For every additional page in length, a book is expected to have an extra 3.4 typos on average.
(B) A 400-page book, on average, should have 3.4 more typos than a 300-page book.
(C) For every additional 3.4 pages in length, a book is expected to have an extra 1.2 typos on average.
(D) The slope has no practical interpretation in this context.

11. Find the predicted number of typos in a 500-page book.: *
(A) 17
(B) 18.2
(C) 171.2
(D) 1701.2

12. Explain what it would mean if an actual 500-page book had a residual of -3.2.: *
(A) This particular book is definitely an outlier and should be dropped from the model.
(B) This particular book had a predicted value smaller than its actual value.
(C) This particular book had a predicted value larger than its actual value.
(D) A mistake has been made since residuals cannot be negative.

36. A study was conducted to see if music has an effect on productivity of workers. The music was turned on during the working hours of 32 randomly selected workers. The workers’ productivity level averaged 82 with a standard deviation of 25. On a different day the music was turned off and there were 50 randomly selected workers. Their productivity level averaged 58 with a standard deviation of 15. What is 90% confidence interval of the difference between the average productivity levels of these 2 groups of workers? : *
(A) (15.94, 32.06)
(B) (16.66, 31.34)
(C) (16.74, 31.26)
(D) Unable to determine because assumptions are not met.

37. Based on previous research, the standard deviation of the distribution of the age at which children begin to walk is estimated to be 1.5 months. A random sample of children will be selected, and the age at which each child begins to walk will be recorded. A 90 percent confidence interval for the average age at which children begin to walk will be constructed using the data obtained from the sample of children. Of the following, which is the smallest sample size that will result in a margin of error of 0.25 month or less for the confidence interval? : *
(A) 95
(B) 100
(C) 135
(D) 140
(E) 240

Questions 25-26: A company claims that their fridges have an average of 22 gallons of useable space inside. You want to see whether they are cheating the consumer. To test this claim, you take a sample of 50 fridges and find the sample mean and sample standard deviation to be 21.2 and 3.0, respectively.

25. What would be the appropriate alternative hypothesis? (Hint: is the customer being cheated if the usable space is too little, too much, or simply different from the assumed amount?): *
(A) Ha: μ = 22
(B) Ha: μ > 21.2
(C) Ha: μ ≠ 22
(D) Ha: μ < 21.2
(E) Ha: μ < 22

26. Compute the appropriate test statistic.: *
(A) -1.8856
(B) -0.2667
(C) 0.2667
(D) 1.8856

: *

Choice (A)
Choice (B)
Choice (C)
Choice (D)
Choice (E)

After numerous studies, it is estimated that the age of college students follows a normal distribution with a mean of 20.7 years and a standard deviation of 1.8 years. A random sample of 16 college students is taken and the sample mean and sample standard deviation are found to be 21.5 years and 2.5 years, respectively.

a. Is the sample average of 21.5 considered an outlier (in other words, what is the chance of getting a sample mean at least as large as 21.5)?

b. The calculated value of the sample standard deviation is larger than σ, is 2.5 years enough larger than 1.8 that the estimate of σ does not seem reasonable?

c. No matter what you got for an answer in part b, assume we no longer trust σ = 1.8 to be valid. Calculate the same probability as you did in part a, but this time, assume that σ is unknown.

d. Is there a significant difference in parts A and C?

Questions 15-18: A multiple regression model was run on a sample of 150 high school students to see whether the heights of their mothers and fathers (in inches) could be used to predict the student’s own height (in inches). Consider the following partial output.
Parameter    Estimate    Standard Error
Intercept    16.967   4.658
Mother    0.299   0.069
Father    0.412   0.051

15. Find the T test for the variable Father.: *
(A) 0.231
(B) 3.643
(C) 4.333
(D) 8.078

16. Choose the best way to interpret the estimated coefficient for Mother.: *
(A) Every extra inch in height of the mother causes the student to be 0.299 inches taller.
(B) Holding the father’s height constant, every additional inch in height from the mother is associated with an increase of 0.299 inches on average in the student’s height.
(C) Holding the father’s height constant, every additional inch in height from the mother is associated with a decrease of 0.299 inches on average in the student’s height.
(D) The coefficient of 0.299 does not have a practical interpretation.

17. Suppose the coefficient for Father turns out to be significant. Choose the best answer: *
(A) A confidence interval for Father would contain 0.
(B) A confidence interval for Father would be completely positive.
(C) A confidence interval for Father would be completely negative.
(D) There is not enough information to tell.

18. Find the 95% confidence interval for Mother.: *
(A) (0.1617, 0.4363)
(B) (0.1626, 0.4354)
(C) (0.1848, 0.4132)
(D) (0.1855, 0.4125)