Question text The price of British Pounds "in US dollars" was 1.5355 last month and is 1.5347 today. Which of the following is TRUE given this information? Select one: a. The value of the US dollar has not changed with respect to the British Pound. b. The British Pound has lost value against the US dollar. c. Turning 100 British Pounds into US dollars today would give you approximately one more dollar compared to the amount of you would have received last month. d. Today, $1000 US dollars would give you approximately 1,535 British Pounds. e. Today, 1000 British Pounds can be converted into approximately $652 US dollars.

A random sample of two variables, x and y, produced the following observations:

Compute the correlation coefficient for these sample data.

Group of answer choices

a. -0.9707

b. -0.2141

c. 0.5133

d. 0.8612

a) The worksheet "Counts8Year" provides the number Top30 TV shows aired on each network by year. Run a two-way ANOVA without replication using the data in columns A to E of the "Counts8Year" worksheet. (Do not include row 1 and check labels.) Two hypothesis tests will be performed, one for the Year (row) factor and the other for the Network (column) factor. What is the value of the test statistic, F_calc, for the test on the Network factor? Provide your answer with 2 decimal places.

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b) R-square (R²) is the proportion of the variation in the data (number of top 30 shows) that can be explained by the factors (year and network). Compute R² = 1 - SSE/SST.   Provide your answer with 4 decimal places.  

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c) What is the conclusion of the ANOVA hypothesis test at a 5% significance level?  (Click to select)At least one pair of network means differ. At least one pair of the yearly means differ.None of the network means differ. None of the yearly means differ.All of the network means differ. All of the yearly means differ.None of the network means differ. At least one pair of yearly means differ.At least one pair of network means differ. None of the yearly means differ.None of the network means differ. All of the yearly means differ.All of the network means differ. None of the yearly means differ.

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d) Based on the ANOVA test results, which means are significantly different? (Click to select)Years 2015 and 2016ABC, CBSFOX, NBCCBS, NBCABC, FOXABC, NBCCBS, FOXNo pairs of means differ significantlyABC, CBS, FOX, NBC

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e) Which of the following methods/test would NOT be appropriate for testing the assumptions of this ANOVA test?

A sample of 44 observations is selected from a normal population. The sample mean is 24, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 23 H1: μ > 23 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? Reject H0 when z > 1.645 Reject H0 when z ≤ 1.645 What is the value of the test statistic? (Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0 Fail to reject H0 e-1. What is the p-value? (Round your answer to 4 decimal places.) e-2. Interpret the p-value? (Round your final answer to 2 decimal places.)

A medical researcher is investigating the effect of drinking coffee on systolic blood pressure. The researcher assumes the average systolic blood pressure is 120 mmHg. For a random sample of 200 patients, the researcher takes two measurements of systolic blood pressure. The first systolic blood pressure measurement is taken during a week when the patients drink no coffee, and the second systolic blood pressure measurement is taken during a week when the patients drink at least two cups of coffee. The medical researcher wonders whether there is a significant difference between the blood pressure measurements.

Which of the following is the correct null and alternative hypothesis for the medical researcher’s study?

1. H₀: µ = 120; H_a: µ ≠ 120
2. H₀: µ = 0; H_a: µ ≠ 0
3. H₀: µ = 0; H_a: µ ≠ 120

Question 2

In a fictional study, suppose that a psychologist is studying the effect of daily meditation on resting heart rate. The psychologist believes the patients who not meditate have a higher resting heart rate. For a random sample of 45 pairs of identical twins, the psychologist randomly assigns one twin to one of two treatments. One twin in each pair meditates daily for one week, while the other twin does not meditate. At the end of the week, the psychologist measures the resting heart rate of each twin. Assume the mean resting heart rate is 80 heart beats per minute.

The psychologist conducts a T-test for the mean of the differences in resting heart rate of patients who do not meditate minus resting heart rate of patients who do meditate.

Which of the following is the correct null and alternative hypothesis for the psychologist’s study?

1. H₀: µ = 80; H_a: µ > 80
2. H₀: µ = 0; H_a: µ ≠ 0
3. H₀: µ = 0; H_a: µ > 0

Question 3

Facebook friends: According to Facebook’s self-reported statistics, the average Facebook user has 130 Facebook friends. For a statistics project a student at Contra Costa College (CCC) tests the hypothesis that CCC students will average more than 130 Facebook friends. She randomly selects 3 classes from the schedule of classes and distributes a survey in these classes. Her sample contains 45 students.

From her survey data she calculates that the mean number of Facebook friends for her sample is: ¯x= 138.7 with a standard deviation of: s=79.3.

She chooses a 5% level of significance. What can she conclude from her data?

1. Nothing. The conditions for use of a t-model are not met. She cannot trust that the p-value is accurate for this reason.
2. We cannot conclude that the average number of Facebook friends for CCC students is greater than 130. The sample mean of 138.7 is not significantly greater than 130.
3. Her data supports her claim. The average number of Facebook friends for CCC students is significantly greater than 130.

Question 4

According to a 2014 research study of national student engagement in the U.S., the average college student spends 17 hours per week studying. A professor believes that students at her college study less than 17 hours per week. The professor distributes a survey to a random sample of 80 students enrolled at the college.

From her survey data the professor calculates that the mean number of hours per week spent studying for her sample is: ¯x= 15.6 hours per week with a standard deviation of s = 4.5 hours per week.

The professor chooses a 5% level of significance. What can she conclude from her data?

1. The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
2. The professor cannot conclude that the average number of hours per week spent studying for students at her college is less than 17 hours per week. The sample mean of 15.6 is not significantly less than 17.
3. Nothing. The conditions for use of a t-model are not met. The professor cannot trust that the p-value is accurate for this reason.

Question 5

An urban planner is researching commute times in the San Francisco Bay Area to find out if commute times have increased. In which of the following situations could the urban planner use a hypothesis test for a population mean? Check all that apply.

1. The urban planner asks a simple random sample of 110 commuters in the San Francisco Bay Area if they believe their commute time has increased in the past year. The urban planner will compute the proportion of commuters who believe their commute time has increased in the past year.
2. The urban planner collects travel times from a random sample of 125 commuters in the San Francisco Bay Area. A traffic study from last year claimed that the average commute time in the San Francisco Bay Area is 45 minutes. The urban planner will see if there is evidence the average commute time is greater than 45 minutes.
3. The urban planner asks a random sample of 100 commuters in the San Francisco Bay Area to record travel times on a Tuesday morning. One year later, the urban planner asks the same 100 commuters to record travel times on a Tuesday morning. The urban planner will see if the difference in commute times shows an increase.

Question 6

The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well.

The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption.

The null hypothesis is that the mean number of insect parts per 100 grams is 75. The alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75.

Is the following a Type I error or a Type II error or neither?

The test fails to show that the mean number of insect parts is greater than 75 per 100 grams when it is.

1. Type I error
2. Type II error
3. Neither

Question 7

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the age of first time expectant mothers. Suppose that CHDS finds the average age for a first time mother is 26 years old. Suppose also that, in 2015, a random sample of 50 expectant mothers have mean age of 26.5 years old, with a standard deviation of 1.9 years. At the 5% significance level, we conduct a one-sided T-test to see if the mean age in 2015 is significantly greater than 26 years old. Statistical software tells us that the p-value = 0.034.

Which of the following is the most appropriate conclusion?

1. There is a 3.4% chance that a random sample of 50 expectant mothers will have a mean age of 26.5 years old or greater if the mean age for a first time mother is 26 years old.
2. There is a 3.4% chance that mean age for all expectant mothers is 26 years old in 2015.
3. There is a 3.4% chance that mean age for all expectant mothers is 26.5 years old in 2015.
4. There is 3.4% chance that the population of expectant mothers will have a mean age of 26.5 years old or greater in 2015 if the mean age for all expectant mothers was 26 years old in 1959.

Question 8

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021.

Which of the following is the most appropriate conclusion?

1. There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.
2. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 14 pounds in 2015.
3. There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 16 pounds in 2015.
4. There is 2.1% chance that the population of expectant mothers will have a mean weight increase of 16 pounds or greater in 2015 if the mean second trimester weight gain for all expectant mothers was 14 pounds in 1959.

Question 9

A researcher conducts an experiment on human memory and recruits 15 people to participate in her study. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.17.

Which of the following is a reasonable interpretation of her results?

1. This suggests that her experimental treatment has no effect on memory.
2. If there is a treatment effect, the sample size was too small to detect it.
3. She should reject the null hypothesis.
4. There is evidence of a small effect on memory by her experimental treatment.

Question 10

A criminal investigator conducts a study on the accuracy of fingerprint matching and recruits a random sample of 35 people to participate. Since this is a random sample of people, we don’t expect the fingerprints to match the comparison print. In the general population, a score of 80 indicates no match. Scores greater than 80 indicate a match. If the mean score suggests a match, then the fingerprint matching criteria are not accurate.

The null hypothesis is that the mean match score is 80. The alternative hypothesis is that the mean match score is greater than 80.

The criminal investigator chooses a 5% level of significance. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.04.

Which of the following is a reasonable interpretation of her results?

1. This suggests that there is evidence that the mean match score is greater than 80. This suggests that the fingerprint matching criteria are not accurate.
2. If there is a treatment effect, the sample size was too small to detect it. This suggests that we need a larger sample to determine if the fingerprint matching criteria are not accurate.
3. She cannot reject the null hypothesis. This suggests that the fingerprint matching criteria could be accurate.
4. This suggests that there is evidence that the mean match score is equal to 80. This suggests that the fingerprint matching criteria is accurate.

Question 11

A group of 42 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.

The group of 42 students in the study reported an average of 5.31 drinks per with a standard deviation of 3.93 drinks.

Find the p-value for the hypothesis test.

The p-value should be rounded to 4-decimal places.

Question 12

Commute times in the U.S. are heavily skewed to the right. We select a random sample of 240 people from the 2000 U.S. Census who reported a non-zero commute time.

In this sample the mean commute time is 28.9 minutes with a standard deviation of 19.0 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.

What is the p-value for this hypothesis test?

Your answer should be rounded to 4 decimal places.

Question 13

Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence to show that this is not true at her university. A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 35 students studied each week was 18.5 hours. The sample standard deviation of 4.3 hours.

Find the p-value.

The p-value should be rounded to 4-decimal places.

Question 14

A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test.

Change: Final Blood Pressure - Initial Blood Pressure

The researcher wants to know if there is evidence that the drug affects blood pressure. At the end of 4 weeks, 36 subjects in the study had an average change in blood pressure of 2.4 with a standard deviation of 4.5.

Find the p-value for the hypothesis test.

Your answer should be rounded to 4 decimal places.

Question 15

Find the p-value for the hypothesis test. A random sample of size 54 is taken. The sample has a mean of 375 and a standard deviation of 83.

H0: µ = 400

Ha: µ< 400

The p-value for the hypothesis test is .

Your answer should be rounded to 4 decimal places.

Question 16

Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester.

In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 39 expectant mothers have mean weight increase of 15.9 pounds in the second trimester, with a standard deviation of 6.0 pounds.

A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds.

Find the p-value for the hypothesis test.

The p-value should be rounded to 4 decimal places.

1. Calculate the payback period for the following investment proposal.
Investment
Annual Net Cash Flows
1
2
3
4
5
6
7
8
9
10
250
86
50
77
52
41
70
127
24
6
40
Payback Period:

2.A 4-year project has a projected cash inflow of $5,000 in the first year, $10,000 in the second year, $15,000 in the third year, and $20,000 in the fourth year. It will cost $19,000 to implement the project. The required rate of return is 25%. What is the NPV?  

Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class Super Saver Deluxe Business Type I $30 $35 -- Room Type II $20 $30 $40 Type I rooms do not have Internet access and are not available for the Business rental class. Round Tree’s management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Summarize the model in algebraic form by defining the decision variables, the objective function and all the constraints. PLEASE DO NOT USE EXCEL TO SOLVE.

Discussion Board Forum 1/Project 2 Instructions

Standard Deviation and Outliers

Thread:

For this assignment, you will use the Project 2 Excel Spreadsheet to answer the questions below. In each question, use the spreadsheet to create the graphs as described and then answer the question.

Put all of your answers into a thread posted in Discussion Board Forum 1/Project 2.

This course utilizes the Post-First feature in all Discussion Board Forums. This means you will only be able to read and interact with your classmates’ threads after you have submitted your thread in response to the provided prompt. For additional information on Post-First, click here for a tutorial. This is intentional. You must use your own work for answers to Questions 1–5. If something happens that leads you to want to make a second post for any of your answers to Questions 1–5, you must get permission from your instructor.

1. A. Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far away from the original 5 and record the new standard deviation.

What is the impact of the new point on the standard deviation? Do not just give a numerical value for the change. Explain in sentence form what happened to the standard deviation. (4 points)

B. Create a data set with 8 points in it that has a mean of approximately 10 and a standard deviation of approximately 1. Use the second chart to create a second data set with 8 points that has a mean of approximately 10 and a standard deviation of approximately 4. What did you do differently to create the data set with the larger standard deviation? (4 points)

2. Go back to the spreadsheet and clear the data values from Question 1 from the data column and then put values matching the following data set into the data column for the first graph. (8 points)

50, 50, 50, 50, 50.

Notice that the standard deviation is 0. Explain why the standard deviation for this one is zero. Do not show the calculation. Explain in words why the standard deviation is zero when all of the points are the same. If you don’t know why, try doing the calculation by hand to see what is happening. If that does not make it clear, try doing a little research on standard deviation and see what it is measuring and then look again at the data set for this question.

3. Go back to the spreadsheet one last time and put each of the following three data sets into one of the graphs. Record what the standard deviation is for each data set and answer the questions below.

                  Data set 1:       0, 0, 0, 100, 100, 100

                  Data set 2:       0, 20, 40, 60, 80, 100

                  Data set 3:       0, 40, 45, 55, 60, 100

Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists. Do not give your calculations in your answer—explain in sentence form. (8 points)

For the last 2 questions, use the Project 1 Data Set.

4. Explain what an outlier is. Then, if there are any outliers in the Project 1 Data Set, what are they? If there are no outliers, say no outliers. (4 points)
5. Which 4 states have temperatures that look to be the most questionable or the most unrealistic to you? Explain why you selected these 4 states. For each state, give both the name and the temperature. (4 points)

Consider two bonds, both with 8% coupon rates (assume annual coupon payments) one with 10 years to maturity and the other with 20 years to maturity. Assume that current market rates of interest are 8%. Calculate the difference in the change of the price of the two bonds if interest rates decrease to 6% one year after purchasing the bond. Repeat the procedure assuming that interest rates increase to 10% one year after purchase. Explain the major bond pricing principle that is being illustrated here

Consider two bonds, both with 8% coupon rates (assume annual coupon payments) one with 10 years to maturity and the other with 20 years to maturity. Assume that current market rates of interest are 8%. Calculate the difference in the change of the price of the two bonds if interest rates decrease to 6% one year after purchasing the bond. Repeat the procedure assuming that interest rates increase to 10% one year after purchase. Explain the major bond pricing principle that is being illustrated here