36. Allied Corporation is trying to determine whether to purchase Machine A or B. It has leased the two machines for a month. A random sample of 5 employees has been taken. These employees have gone through a training session on both machines. Below you are given information on their productivity rate on both machines. (Let d = Machine A - Machine B.)Productivity Rate

please explain and show all work --- do NOT use excel commands/excel to solve this problem

a.         State the null and alternative hypotheses for a two-tailed test.

            b.   Find the mean and standard deviation for the difference.

            c.   Compute the test statistic.

            d.   Test the null hypothesis stated in Part a at the 10% level.

A survey of 29 smokers showed that they smoke an average of 13 packs per week. If the data follows a normal distribution with a standard deviation of 3 packs per week, find the 99% confidence interval for the true average of packs smoked per week.

According to past data, the 15% of all college students in California are business majors. Suppose a random sample of 200 California college students is taken.

a) What information about this sample allows us to use the normal distribution for our sampling distribution?

b) Calculate the standard error. Round to two places for ease.

c) What is the probability that the sample of 200 gives a sample proportion of 18% or higher? Show your calculator function and entries. Round to 4 places.

A study considered the question, "Are you a registered voter?" Accuracy of response was confirmed by a check of city voting records. Two methods of survey were used: a face-to-face interview and a telephone interview. A random sample of 88 people were asked the voter registration question face to face. Of those sampled, seventy-one respondents gave accurate answers (as verified by city records). Another random sample of 90 people were asked the same question during a telephone interview. Of those sampled, seventy-one respondents gave accurate answers. Assume the samples are representative of the general population.

Let p1 be the population proportion of all people who answer the voter registration question accurately during a face-to-face interview. Let p2 be the population proportion of all people who answer the question accurately during a telephone interview. Find a 90% confidence interval for p1 – p2. (Use 3 decimal places.)

lower limit

upper limit

Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. The Hill of Tara is a very important archaeological site in Ireland. It is by legend the seat of Ireland's ancient high kings†. Independent random samples from two regions in Tara gave the following phosphorous measurements (ppm). Assume the population distributions of phosphorous are mound-shaped and symmetric for these two regions.

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to one decimal place.)

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find an 80% confidence interval for μ₁ − μ₂. (Round your answers to one decimal place.)

A car manufacturer claims that 52% of Americans are interested in having internet access in their cars. In a simple random sample of 300 Americans, 161 stated they were interested in having web access in their cars. Test the hypothesis that more than 52% of Americans are interested in having internet access in their cars. Assume independence. Use .05 as the level of significance.

Complete the steps below:

a) Write the null and alternative hypotheses using proper notation.

b) Explain how each of the conditions of CLT are met.

c) Give the z-test statistic AND the p-value.

d) Using your p-value, what is your decision about the null hypothesis.

e) What is your conclusion regarding whether or not more than 52% of Americans are interested in having web access in their cars? Be sure to use the phrase statistically significant.  

The following table shows the information for a sample of 50 companies in the primary
industry. The variable Sector indicates the sector in which the company is operating and
the variable Company size indicates the size of the company in terms of its annual turnover.
Sector Company size Sector Company size
1. Fishing Large 26. Fishing Medium
2. Fishing Medium 27. Fishing Large
3. Agriculture Medium    28. Fishing Medium
4. Fishing Large 29. Fishing Medium
5. Agriculture Medium 30. Agriculture Small
6. Fishing Large    31. Agriculture Large
7. Agriculture Small 32. Fishing Medium
8. Mining Large 33. Fishing Large
9. Mining Small 34. Fishing Large
10. Mining Large 35. Agriculture Medium
11. Agriculture Medium 36. Agriculture Large
12. Agriculture Medium 37. Agriculture Medium
13. Mining Large 38. Mining Large
14. Agriculture Small 39. Fishing Small
15. Fishing Medium    40. Agriculture Medium
16. Fishing Large    41. Mining Small
17. Agriculture Medium    42. Mining Medium
18. Fishing Medium 43. Agriculture Medium
19. Mining Medium    44. Mining Large
20. Fishing Medium 45. Fishing Large
21. Fishing Small 46. Mining Small
22. Mining Small    47. Mining Medium
23. Agriculture Small 48. Agriculture Medium
24. Mining Large 49. Mining Large
25. Agriculture Small 50. Mining Large

Use the information in the table above to answer the following questions.
a) For each of the two random variables, state whether it is a qualitative or
quantitative variable.
b) For each of the two random variables, state the scale of measurement.
c) Construct a cross tabulation table between Sector (rows) and Company size
(columns).
d) What is the probability that a randomly selected company is a large company?
e) What is the probability that a randomly selected company operate in the fishing
sector?
f) What is the probability that a randomly selected company is a medium size and it
operates in the agriculture sector?
g) What is the probability that a randomly selected company is either a small company
or a mining sector company or both?
h) What is the probability that a randomly selected company is either a small company
or a large company or both?
i) What is the probability that a randomly selected company is a small and large
company?
j) What is the probability that a randomly selected company is not a fishing sector
company?
k) What is the probability that a randomly selected company is not a medium size
company?
l) What is the probability that a randomly selected company is a mining sector
company if it is known that the company is a medium sized company?
m) If it is known that a company operate in the mining sector, what is the probability
that it is a medium size company?
n) Is company size statistically independent of sector in which the company operate?
Motivate.
o) If we define A = event company small and B = event company is large; are the events
A and B mutually exclusive? Motivate.

A coin is tossed 400 times, landing heads up 219 times. Is the coin fair?

Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time. ​$434 per month invested at 4​%, compounded​ monthly, for 5 ​years; then ​$787 per month invested at 5​%, compounded​ monthly, for 5 years.

Problem 5. Sampling from two populations produced the following results. ?̅ =385 Sx=30 nx =100

?? = 3 7 8 S y = 2 5 n y = 9 0

1. Find the standard error of (?̅ - ??). Show your calculations.

2. Find the 90% confidence interval estimate for the difference between the two population means.

   Show your calculations.

3. State clearly the assumption(s) that are necessary for your answer to (b) will be valid.

4. Interpret your result in (b).

5. It is claimed that the two population means are not different from each other. Do you reject this

   claim? Explain clearly.

Let X be the population of house prices in a large city. Assume that the population distribution of house prices is normal [i.e., X ~ N(μ, σ2)]. A random sample of 10 house prices (in thousands of $) provided the following data:

      90    100   115   72    125   95    105   135   120   88

1. Find the standard error of the sample mean (?̅). Show your calculations.

2. Write out the null and alternative hypotheses for determining whether the population mean

   differs from 90 (thousand $).

3. Write out the decision rule for the question in (b).

4. Find the calculated test-value for the question in (b). Show your calculations.

5. Find the 10%, 5%, and 1% critical values for the question in (b).

6. Do you reject the null hypothesis in (b)? Explain clearly.

7. The p-value for the question in (b) is 0.041. What does the p-value mean, and how does it

   change your conclusion in (f)? Explain clearly.

A college dean is interested in the exam performance of students in a History course. After the final exam, students are randomly selected from three different section of the History course. What can be conclude with an α of 0.01? The data are below.

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

At least on section differs on the final exam.None of the sections differ on the final exam.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =  ; significant:  ---Select--- Yes No
1 vs. 2: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
1 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

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Question 7 of 10

Exercise 12.39

A box contains billions of tickets, all labeled either 2, 3, or 5. A simple random sample of 400 tickets is taken; the sample mean is 3.6 and the sam- ple SD is 1. Let μ represent the population mean. Which of the following statements are correct?

A. The interval between 3.55 and 3.65 is a 90% confidence interval for μ. B. There is a 90% probability that μ is between 3.55 and 3.65.
C. There is a 95% probability that μ is between 3.5 and 3.7.
D. The interval between 3.5 and 3.7 is a 95% confidence interval for μ.

A blind taste test is conducted to determine which of two​ colas, Brand A or Brand​ B, individuals prefer. Individuals are randomly asked to drink one of the two types of cola​ first, followed by the other​ cola, and then asked to disclose the drink they prefer. Results of the taste test indicate that 42 of 100 individuals prefer Brand A. Complete parts a through c. ​(a) Conduct a hypothesis test​ (preferably using​ technology) Upper H 0​: p equals p 0 versus Upper H 1​: pnot equalsp 0 for p 0equals0.31​, 0.32​, 0.33​, ​..., 0.51​, 0.52​, 0.53 at the alphaequals0.05 level of significance. For which values of p 0 do you not reject the null​ hypothesis? What do each of the values of p 0 ​represent? Do not reject the null hypothesis for the values of p 0 between nothing and nothing​, inclusively. ​(Type integers or decimals as​ needed.)