The following table gives the weights, to the nearest kilogram, of randomly-selected male university students. 69 82 75 66 72 63 74 78 73 79 70 74 68 74 76 72 84 63 69 78 81 60 77 83 73 86 71 68 76 70 68 80 73 67 71 75 78 73 64 73 a. Using class intervals of size 5kg, construct a frequency distribution of the above data. b. Using the grouped data, calculate the following quantities: iv. Quartile number 1 v. Quartile number 3 vi. Variance vii. Standard Deviation (1 mark)

1. According to a social media​ blog, time spent on a certain social networking website has a mean of 17 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 7 minutes.
   1. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 16.5 and 17.5 minutes?
2. A global research study found that the majority of​ today's working women would prefer a better​ work-life balance to an increased salary. One of the most important contributors to​ work-life balance identified by the survey was​ "flexibility," with 41​% of women saying that having a flexible work schedule is either very important or extremely important to their career success. Suppose you select a sample of 100 working women.

What is the probability that in the sample between 33​% and 48​% say that having a flexible work schedule is either very important or extremely important to their career​ success?

3. A survey found that 27​% of consumers from a Country A are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more sustainable. Suppose you select a sample of 100 respondents from Country A. Complete parts​ (a) through​ (d) below.

What is the probability that in the​ sample, between 23​% and 31​% are more likely to buy stock in a company based in Country​ A, or shop at its​ stores, if it is making an effort to publicly talk about how it is becoming more​ sustainable?

1. Given the following linear programming model, answer the questions that follow. You are given the result of a computer program. The results are

Maximize 9 X₁ + 12 X₂ + 10 X₃

Subject to:

Machine Constraint:   3 X₁ + 4 X₂ + 3 X₃ < 160

Labor Constraint:        6 X₁ + 10 X₂ + 4 X₃ < 288

Materials Constraint: 2 X₁ + 2 X₂ + 7 X₃ < 200

Product 2 Constraint: X₁ < 16

OPTIMAL SOLUTION

Objective Function Value =         483.097

      Variable             Value             Reduced Costs  

   --------------     ---------------      ------------------

         X1                    16.000                   0.000

         X2                    10.839                   0.000

         X3                    20.903                   0.000

     Constraint        Slack/Surplus           Dual Prices   

   --------------     ---------------      ------------------

         1                      5.935                   0.000

         2                      0.000                   1.032

         3                      0.000                   0.839

         4                      0.000                   1.129

OBJECTIVE COEFFICIENT RANGES

    Variable       Lower Limit       Current Value     Upper Limit

------------   ---------------    --------------- ---------------

      X1                  7.871              9.000   No Upper Limit

      X2                  2.857             12.000           14.059

      X3                  4.800             10.000           18.750

RIGHT HAND SIDE RANGES

  Constraint      Lower Limit       Current Value     Upper Limit

------------   ---------------    --------------- ---------------

       1                154.065            160.000   No Upper Limit

       2                192.000            288.000          304.727

       3                 70.400            200.000          226.286

       4                  0.000             16.000           30.154

1. If the profit of Product 3 was changed to $20 and the profit of Product 1 was changed $20, would that change the solution?   Provide proof.

2. If the number of minutes of Machine time was decreased to 155 minutes and the amount of materials were decreased to 170 pounds, would this change the solution? Provide proof.

3. The Dual Price for Constraint 1 (Machine time) is 4.2. In terms of this problem what does that mean?

For this activity, select a recurring quantity from your OWN life for which you have monthly records at least 2 years (including 24 observations in the dataset at least). This might be the cost of a utility bill, the number of cell phone minutes used, or even your income. If you do not have access to such records, use the internet to find similar data, such as average monthly housing prices, rent prices in your area for at least 2 years (You must note the data source with an accessible link). Data can also be monthly sales of some particular commodity. 1.4 Please do the descriptive analysis, using the method of index number and Exponential Smoothing individually. And try to explain the pattern you find. 1.5 Use two methods you learned to predict the value of your quantity for the next year (12 months). And make a comparison with two results.

2. One personality dimension that seems well recognized by most people is that of introversion-extroversion. Extroverts are described as outgoing, sociable, and fun-loving, whereas introverts are described as reserved and less sociable. Because introverts seem more directed toward their own thoughts and ideas, we might suspect that introverts and extroverts may respond differently to external stimulation such as noise. To more fully investigate this issue, Standing, Lynn, and Moxness (1990) used a 2 ✕ 2 between-subjects design to vary personality type (factor A), introverts and extroverts, and background noise (factor B), quiet and noisy, while subjects performed a reading comprehension task. Suppose you conducted a similar study with 12 subjects per cell, and each person completed a 15 item true-false reading comprehension task. A person’s score was the number of items correctly answered. You obtained the following scores:

2.a.What is the relationship between personality type and the effect of background noise? Use α= .05. If an interaction occurred, use the Tukey HSD test for the simple effects.

2.b.Plot the cell means with the appropriate labelling. You can draw this by hand.

2.c.Report the results as it would appear in a research paper.  

Grades on a standardized test are known to have a mean of 940 for students in the United States. The test is administered to 436 randomly selected students in​ Florida; in this​ sample, the mean is 952.22 and the standard deviation ​(s​) is 101.52.

The​ 95% confidence interval for the average test score for Florida students is ​(__ , __). ​(Round your responses to two decimal places.​)

The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions:

A.            If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes?

B.            If you randomly select 75 people what is the probability that their average wait time will be between 23 and 26 minutes?

C.            If you randomly select 100 people what is the probability that their average wait time will be at most 24 minutes?

Your measure of intelligence test booklet says that X= 100 (SD = 15). Using that information, match the following terms with its numerical value. Match

Mean _____ 1. 55 - 145

68% sure the true scores lies in the range of ___________ 2. 100

standard deviation _________ 3. 70 - 130

99% sure the true scores lies in the range of ________ 4. 85 - 115

95 % sure the true scores lies in the range of ________ 5. 15

Suppose that at the beginning of March, a new strain of flu, flu-A, emerges and begins to spread through U-College undergraduates. The symptoms of Flu-A are like the common flu, flu-B, and other respiratory illnesses. It is thought that the infection rate of Flu-A will be similar to that of Flu-A at other colleges, but that the disease will be much less deadly. Flu-A is expected to infect about 20 out of every 1,000 undergraduate students per month for the rest of the semester, while the flu-B is expected to infect about 30 out of every 1,000 undergraduates per month for the rest of the semester. Assume that this rate remains the same for each of the remaining months in the semester (March, April, and May). There are currently 6,800 U-College undergraduates on campus. You may assume that infection with Flu-A is independent of infection with the flu-B.

1. Calculate the total expected number of Flu-A cases among U College undergraduates over the next three months.

2. If more than 150 cases of Flu-A are observed among the undergraduates during the next month, the College will go into shut-down mode and cancel class meetings. What is the probability the College goes into shut-down mode by the end of March?

Suppose you estimate a simple linear regression model and obtain a t-value for the slope coefficient of -3.1. Based on this, explain which of the following statements are correct or wrong:

a) A 95% confidence interval for the true slope would exclude 0.
b) It is possible that the point estimate for the slope is b_1=4.
c) At the 10% level of significance you fail to reject the null hypothesis that the true slope is equal to 0.
d) The probability that the true slope is negative is greater than the probability that the true slope is positive.

statistics and probability questions, solve clearly, show steps and in 30 minutes for thumbs up vote

A government report on remuneration for university administrators in Canada lists average salaries for various executive roles. The total annual salary for university presidents is listed as $500,000. To test this reported figure, at LOC = 95%, a random sample of 16 Canadian university presidents’ total annual salaries was collected. The raw data is below (in $/year):
618,000, 464,000, 686,000, 500,000, 746,000, 704,000, 596,000, 629,000,
523,000, 756,000, 561,000, 608,000, 691,000, 663,000, 529,000, 442,000.
a) Find the mean and standard deviation using a spreadsheet.
b) Assess the government report’s claim, using the critical-value method.
c) Use the p-value method to determine if there are any commonly-used LOC values for which the conclusion would be opposite to your answer from Part (a).

statistics and probability questions, solve clearly, show steps and in 30 minutes for thumbs up vote

please answer all parts of the question, garunteed thumbs up.

A proposal to amalgamate the two towns of Smallville and Palookatown into one municipality is scheduled to be put to a referendum vote at the next local election. A random survey of 200 voters in each town is conducted, with 113 voters in Smallville indicating their support for the proposal, and 90 voters in Palookatown indicating their support.
a) Find the proportion of voters in support of amalgamation for both towns.
b) Calculate confidence intervals for the difference between the levels of support for amalgamation in the two towns, for:
i. LOC = 95%
ii. LOC = 99%
c) Comment on whether or not the results from Part (a) support the idea that one town is more supportive, overall, of the amalgamation proposal.
d) Assume that this data was collected after a claim was made that the level of support is different in the two towns. Test this claim at LOC = 95%, using the critical value method.
e) Use the p-value method to determine if your decision from Part (d) above would change for any of
α = 0.10, 0.01, 0.005, 0.001 .
f) Assuming that the sampling in this study was done in a random and unbiased manner, do you think that the level of support for amalgamation is equal in the two towns, or are observed differences probably just attributable to random sampling error? Explain in the context of your answers above (Note: there is no single right answer to this question – but your answer needs to be consistent with the arguments supporting it).

statistics and probability questions, solve clearly, show steps and in 30 minutes for thumbs up vote

A local manufacturer of wooden furniture orders timber from nearby mills, to make their various products such as tables, chairs, and bedframes. One of the woodworkers there expresses their dissatisfaction with the quality of the timber supplied by the mills, and states that in their opinion, more than half of their timber pieces of a certain size range contain unworkable flaws.
a) Test this claim, at LOC = 90%, against a subsequent random sample of 50 timber pieces in this size range, of which 24 pieces contain unworkable flaws. Use the critical-value method.
b) Use the p-value method to determine if the result from Part (a) would be different for any other common LOC.

1

The number of goals in a World Cup soccer match has a Poisson distribution with a mean of 3. For a soccer player in World Cup, the probability of having an age over 30 is 0.2.

a. What is the probability of having 0 goal in a World Cup soccer match? (3 pts) What is the probability of having more than 1 goal in a World Cup soccer match?

b. What is the probability that 0 out of the 11 players in a World Cup soccer team are older than 30 ?

c. The probability that a soccer team wins a World Cup match is 0.7 if none of its players are older than 30. The probability that a soccer team wins a World Cup match is 0.4 if some players are older than 30. The probability that “no players are older than 30 in a World Cup soccer team” is your result from question b. A soccer team just won the latest World Cup match. Given this information, what is the probability that NO players in the team have an age over 30?

Fear of breast cancer. A recent survey of 1000 American women ages 45-64 asked them what medical condition they feared the most. 61% said that they feared breast cancer the most. Construct a 95% confidence interval for the population proportion of women who most feared breast cancer. Then Interpret the confidence interval.