For the next 3 questions, please read the description below. Researchers want to estimate the mean monthly electricity bill in a large urban area using a simple random sample of 100 households. Their calculation shows that the sample standard deviation is $15.50.

*Assume that the population standard deviation is unknown.What is the error of estimate for a 99% confidence interval?

answer choices 3.67 4.07 3.99 4.73

*Assume that the population standard deviation is known to be $30. The average monthly electricity bill of the 100 households is $120. What is the upper bound for a 90% confidence interval?

answer choices 124 122 125 123

*Assume that the population standard deviation is unknown. If the researchers want to decrease the error of estimate, which of the following number of households is more likely to be their sample size?

answer choices 30 100 90 120

1)         The population standard deviation for waiting times to be seated at a restaurant is known to be 10 minutes. An expensive restaurant claims that the average waiting time for dinner is approximately 1 hour, but we suspect that this claim is inflated to make the restaurant appear more exclusive and successful. A random sample of 30 customers yielded a sample average waiting time of 50 minutes.

1. Is there evidence to say that the restaurant’s claim is too high? Insert the results from StatCrunch here.

2. State the hypotheses, your decision and conclusion. Include the reason for your decision using the output from above.

3. The original data (individual waiting times) is not normally distributed. What theorem allows us to do the calculations in part (a)?

2)         A sample of 800 items produced on a new machine showed that 48 of them are defective. The factory will get rid the machine if the data indicates that the proportion of defective items is significantly more than 5%. At a significance level of 10% does the factory get rid of the machine or not?

1. Insert the results from StatCrunch here.

2. State the hypotheses, your decision and conclusion. Include the reason for your decision using the results from above.

3)         A psychologist claims that the mean age at which children start walking is 12.5 months. The following data give the age at which 18 randomly selected children started walking.

15        11        13        14        15        12        15        10        16

17        14        16        13        15        15        14        11        13

1. Test at the 1% level of significance if the mean age at which children start walking is different from 12.5 months. Insert the results from StatCrunch here.

2. State the hypotheses, state your decision and conclusion. Include the reason for your decision from the results above.

4)         According to a study, 107 of 507 female college students were on a diet at the time of the study.

a) Construct a 99% confidence interval for the true proportion of all female students who were on a diet at the time of this study. Insert the results from StatCrunch here.

b) Interpret this interval.

c) Is it reasonable to think that only 17% of college women are on a diet? Why or why not?

The data from data217.dat contains information on 78 seventh-grade students. We want to know how well each of IQ score and self-concept score predicts GPA using least-squares regression. We also want to know which of these explanatory variables predicts GPA better. Give numerical measures that answer these questions. (Round your answers to three decimal places.)
(Regressor: IQ) R ^{2 ANSWER 1}


(Regressor: Self-Concept) R ^{2 : ANSWER 2}

Which variable is the better predictor?

IQSelf Concept Answer 3

obs     gpa     iq      gender  concept
1       7.94    118     2       66
2       8.292   104     2       60
3       4.643   83      2       47
4       7.47    120     2       55
5       8.882   90      1       67
6       7.585   104     2       59
7       7.65    104     2       75
8       2.412   107     2       58
9       6       114     1       55
10      8.833   107     2       101
11      7.47    116     1       59
12      5.528   91      1       73
13      7.167   120     2       38
14      7.571   114     1       57
15      4.7     117     1       35
16      8.167   114     1       58
17      7.822   123     1       53
18      7.598   132     1       56
19      4       90      2       49
20      6.231   111     1       68
21      7.643   125     2       92
22      1.76    74      2       35
24      6.419   118     1       48
26      9.648   123     2       74
27      10.7    118     1       103
28      10.58   112     2       67
29      9.429   103     2       64
30      8       123     2       82
31      9.585   125     2       59
32      9.571   121     1       50
33      8.998   117     1       60
34      8.333   122     1       70
35      8.175   108     2       63
36      8       111     2       77
37      9.333   118     1       55
38      9.5     125     2       61
39      9.167   127     2       45
40      10.14   129     1       83
41      9.999   140     1       46
43      10.76   126     2       74
44      9.763   124     2       56
45      9.41    127     2       51
46      9.167   122     2       69
47      9.348   107     2       71
48      8.167   124     2       84
50      3.647   97      2       43
51      3.408   125     1       22
52      3.936   88      2       25
53      7.167   118     2       70
54      7.647   123     2       50
55      .53     80      2       37
56      6.173   95      2       64
57      7.295   105     2       57
58      7.295   99      1       58
59      8.938   124     1       80
60      7.882   103     1       50
61      8.353   101     2       36
62      5.062   92      2       69
63      8.175   117     2       75
64      8.235   118     2       67
65      7.588   114     2       39
68      7.647   113     2       43
69      5.237   109     1       53
71      7.825   97      2       61
72      7.333   99      1       61
74      9.167   129     2       70
76      7.996   120     2       63
77      8.714   103     1       45
78      7.833   111     1       41
79      4.885   108     2       67
80      7.998   98      1       65
83      3.82    102     2       56
84      5.936   101     1       48
85      9       118     1       37
86      9.5     115     1       50
87      6.057   108     2       32
88      6.057   105     1       63
89      6.938   107     2       49

The Mean life expectancy of Men in the U.S. is 78 years , with a population standard deviation of 7 years. A new study is using a random sample of 64 men to study life expectancy.

A. What is the Shape, Mean (expected value) and standard deviation of the sampling distribution of the sample mean for this study?

B. What is the probability that the sample mean will be larger than 80 years?

C. What is the probability that the sample mean will be less than 80 years?

A study was undertaken to investigate the effectiveness of an aquarobic exercise program for patients with osteoarthritis. A convenience sample of 70 individuals with arthritis was selected, and each person was randomly assigned to one of two groups. The first group participated in a weekly aquarobic exercise program for 8 weeks; the second group served as a control. Several pieces of data were collected from the individuals, including their total cholesterol (mg).

Determine if there is a significant difference in the mean cholesterol for the two groups (aquarobic & control) at the start of the study using a significance level of 0.10.   

• What hypotheses should be tested? Make sure to select the hypotheses which are written with notation consistent with the type of samples selected.

  Ho:μ1=μ2Ho:μ1=μ2
  Ha:μ1>μ2Ha:μ1>μ2

  Ho:μ1=μ2Ho:μ1=μ2
  Ha:μ1≠μ2Ha:μ1≠μ2

  Ho:μd=0Ho:μd=0
  Ha:μd≠0Ha:μd≠0

  Ho:μ1=μ2Ho:μ1=μ2
  Ha:μ1<μ2Ha:μ1<μ2

  Ho:μd=0Ho:μd=0
  Ha:μd<0Ha:μd<0

  Ho:μd=0Ho:μd=0
  Ha:μd>0Ha:μd>0

• αα  =
• TS: t =   (round to 3 decimal places)
• probability = Select an answer 0.4497 0.8994 0.5503
• decision: Select an answer reject H₀ fail to reject H₀
• What conclusion is reached based upon the decision made in your test?
  • At the 0.10 level, there is not sufficient evidence to conclude there is a difference in the mean cholesterol of individuals participating in the aquarobic program and those in the control group.
  • At the 0.10 level, there is sufficient evidence to conclude there is a difference in the mean cholesterol of individuals participating in the aquarobic program and those in the control group.

After the 8-week program, those who participated in the aquarobic program had their ending cholesterol measured, and the change in cholesterol was recorded for each participant. Estimate the mean cholesterol change using 90% confidence.

• The formula which should be used for this interval is:
  • (¯y1−¯y2)±t√s21n1+s22n2(y¯1-y¯2)±ts12n1+s22n2
  • ¯yd±tsd√ndy¯d±tsdnd
• With % confidence, we estimate that the mean cholesterol before participating in 8 weeks of aquarobics is between mg and mg  than the mean cholesterol after participation. Note: Round the limits of your interval to three decimal places. In the last box type the appropriate word - more or less. Think carefully about what positive and negative differences mean about the change in cholesterol based on how the differences were taken.

A 90% confidence interval was also calculated for the change in total cholesterol (pre - post) for the control group. That interval was found to be (-2.005, 2.192). Based on this interval and the one which you calculated for the aquarobic group, what conclusion would you draw?

• Neither group had a significant change in mean cholesterol.
• The control group did not have a significant change in mean cholesterol, while the aquarobic group had a significant decrease in mean cholesterol.
• The mean cholesterol for the control group increased, while the aquarobic group had a significant decrease in mean cholesterol.
• Both groups had a significant decrease in mean cholesterol. However, the decrease for the aquarobic group was larger.
• The aquarobic group did not have a significant change in mean cholesterol, while the control group had a significant increase in mean cholesterol.

1. An experiment examined the impact of THC (the active ingredient in marijuana) on various physiological and psychological variables. The study recruited a sample of 18 young adults who were habitual marijuana smokers. Subjects came to the lab 3 times, each time smoking a different marijuana cigarette: one with 3.9% THC, one with 1.8% THC, and one with no THC (a placebo). The order of the conditions was randomized in a double-blind design.

At the start of each session, no subject reported being “high.” After smoking the cigarette, participants rated how “high” they felt, using a positive continuous scale (0 representing not at all “high”). For the placebo condition, participants reported a mean “high” feeling of 11.3, with a standard deviation of 15.5. Is there evidence of a significant placebo effect, with subject feeling significantly “high” after smoking a placebo marijuana cigarette?

the appropriate null and alternative hypotheses for this study- H₀: m = 0 versus H_a: m > 0

a. What is the appropriate statistic to test this hypothesis? What is its value?

b. what is the P-value for the appropriate test? Specify the distribution used and all relevant parameters.

1.) In a recent​ survey,66​% of the community favored building a police substation in their neighborhood. If 14 citizens are​ chosen, find the probability that exactly 5 of them favor the building of the police substation. Round the answer to the nearest thousandth.

a.) .357

b.) .660

c.) .015

d.) .216

2.) A coin is tossed. Find the probability that the result is heads.

a.) .5

b.) .1

c.) 1

d.) .9

3.) The mean SAT verbal score is 464 with a standard deviation of 90. Use the empirical rule to determine what percent of the scores lie between 284 and 554. Assume the data set has a bell-shaped distribution.

a.) 68%

b.) 83.9%

c.) 34%

d.) 81.5%

Please answer all three questions! Thank you!

Please use the following information for Questions 2, 3, and 4.

To determine whether there was a relationship between the region of the world that you live in and the amount of beer that you drink, suppose we took 3 samples of 25 people per region from Asia, Europe and America.

2) If we let µ₁, µ₂, and µ₃ be the average calcium intake per day in milligrams for people with diagnosed osteopenia, osteoporosis or neither (healthy controls), respectively, the appropriate hypotheses in this case are:

a) H₀: μ₁ = μ₂ = μ₃

H_a: μ₁, μ₂, μ₃, are not all equal

b) H₀: μ₁, μ₂, μ₃, are not all equal

H_a: μ₁ = μ₂ = μ₃

c) H₀: μ₁ ≠ μ₂ ≠ μ₃

H_a: μ₁ = μ₂ = μ₃

d) None of the above are correct.

3) Here are the three sample standard deviations for the calcium intake for the three groups (osteopenia, osteoporosis or neither (healthy controls)):

Based on this information, do the data meet the condition of equal population standard deviations for the use of the ANOVA?

a) Yes, because 287.7 - 147.2 < 2.

b) Yes, because 287.7147.2<2287.7147.2<2.

c) No, because 287.7 - 147.2 > 2.

d) No, because the standard deviations are not equal.

4)

The analysis was run on the data and the following output was obtained:
ANOVA table

Based on this information, we :

a) Fail to reject the H₀ and conclude that the data do not provide sufficient evidence that there is a relationship between calcium intake and bone health.

b) Fail to reject the H₀ and conclude that the data provide strong evidence that the three means (representing calcium intake and bone health) are not all equal.

c) Reject the H₀ and conclude that the data provide strong evidence that there is a relationship between between calcium intake and bone health.

d) Reject the H₀ and conclude that the data provide strong evidence that calcium intake is related to bone health in the following way: the mean for healthy people is higher than the mean for people with Osteopenia, which in turn is higher than that for people with Osteoporosis.

Cats are visual animals and enjoy watching on-line videos. A new on-line video enhanced for feline viewing is being developed. The mean time that a cat will view the video in one setting is under study. The nine cats in the study viewed the video for 82 seconds on average with a standard deviation 18 seconds. Use this information to answer the questions below.

1. What is the parameter in this situation?
2. What is the point estimate for the parameter in this case?
3. What is the standard error for the point estimator in this case?
4. What is the set of hypotheses that would be used to test that the mean viewing time is 90 seconds against the alternative that the mean viewing time differs from 90 seconds?
5. What is the value of the test statistic to test the null hypothesis that the mean viewing time is 90 seconds?
6. What is the name of the distribution of the test statistic if the mean viewing time really is 90 seconds? This is the set of values possible for the test statistic when the null hypothesis is true.
7. What value must the test statistic be more extreme than in order to reject the null hypothesis at the 1% significance level?
8. What is the value of the p-value in this case? State a range of values, not a specific value. Hint: The p-value is the tail areas associated with the test statistic, that is the area below the negative and the area above the positive.
9. What is the decision about the null hypothesis in this case with a significance level of 1%? Hint: If the p -value is less than the significance level then reject the null hypothesis. The p-value is the chance that you are wrong if you reject the null hypothesis based on these data.
10. What is the conclusion about the alternative hypothesis, based on the decision above about the null hypothesis? Write a sentence that begins, Conclude, the data… .
11. What is the 99% confidence interval to estimate the parameter based on these data?
12. Does the above confidence interval contain the hypothesized parameter value in this case? Write a sentence about what the confidence interval indicates about the parameter value.

The roulette wheel has 38 slots. Two of the slots are green, 18 are red, and 18 are black. A ball lands at random in one of the slots. A casino offers the following game. Pay $1 to enter the game. If the ball falls on black, you don’t get anything, if the ball falls on green, you get a dollar, if the ball falls on red, you get $1.95. Bob plays this game 100 times, and of course, the 100 outcomes are independent. What is the probability that he comes out ahead?

#15

How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars).

(b) Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + SS_W. (Use 3 decimal places.)

Find d.f._BET, d.f._W, MS_BET, and MS_W. (Use 3 decimal places for MS_BET, and MS_W.)

Find the value of the sample F statistic. (Use 3 decimal places.)


What are the degrees of freedom?
(numerator)
(denominator)

(f) Make a summary table for your ANOVA test.

University magazine agency wants to determine the best combination of two possible magazines to print for the month of May. Star which the University has published in the past with great success is the first choice under consideration. Prime is a new venture and is a promising magazine. The university envisages that by positioning it near Star, it will pick up some spillover demand from the regular readers. The University also hopes that the advertising campaign will bring in a new type of reader from a potentially very lucrative market. The publishing department wants to print at most 500 copies of Star and 300 copies of Prime. The cover price for Star is $3.50, the university is pricing Prime for $4.50 because other magazines doing the same line of business command this type of higher price. The University publishing department has 25 hours of printing time available for the production run. It has 27.5 hours for the collation department, where the magazines are actually assembled. Each copy of Star magazine requires 2.5 minutes to print and 3 minutes to collate. Each Prime requires 1.8 minutes to print and 5 minutes to collate. How many of each magazine should the University print to maximize revenue? Show all the corner solutions and the value of the objective function.

Shows work please!

Hint: You are required to maximize revenue assuming that Star = X and Prime = Y. create a table, specify the LP, draw graph to show feasible region and solve for the corner points. Find the profit for each of the solutions. Also convert hours to minutes in the constraints. The problem has 4 constraints excluding the non-negative constraints.

a. Formulate a linear programming model for this problem. (15 points)

b. Represent this problem on a graph using the attached graph paper. Show the feasible region. (10 points)

c. Solve this model by using graphical analysis showing the optimal solution and the rest of the corner points as well as the profits. (25 points)

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 170 engines and the mean pressure was 6.7 pounds/square inch (psi). Assume the population standard deviation is 1.0. If the valve was designed to produce a mean pressure of 6.6 psi, is there sufficient evidence at the 0.05 level that the valve performs above the specifications?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6:

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

Step 3 of 6:

Specify if the test is one-tailed or two-tailed.

Step 4 of 6:

Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6:

Identify the level of significance for the hypothesis test.

Step 6 of 6:

Make the decision to reject or fail to reject the null hypothesis

A sample of 250 observations is selected from a normal population with a population standard deviation of 23. The sample mean is 18

1. Determine the standard error of the mean. (Round your answer to 3 decimal places.)
2. Determine the 99% confidence interval for the population mean. (Use z Distribution Table.) (Round your answers to 3 decimal places.)