An agent for a residential real estate company in a large city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:

(a) Determine the coefficient of determination, r², and interpret its meaning.

(b) Determine the standard error of the estimate (Syx).

(c) How useful do you think this regression model is for predicting the monthly rent?

(d) Can you think of other variables that might explain the variation in monthly rent?

In 2016, the World Health Organization estimated that the average obesity rate worldwide was 13%[1]. (This includes all countries of the world, not just the countries in the sample.)

[1] Source: World Health Organization.

1. Using the sorted data, determine the probability that a randomly selected country from the sample has an obesity rate greater than the worldwide rate. Show your work and round your answer to the nearest thousandth.

2. Examining the dataset, can you suggest a reason for the high proportion of countries in the dataset having an obesity rate above the worldwide average? State your reason(s) below:

3. Suppose that fifteen of the countries from the dataset were going to be randomly selected for a study to see if the obesity rates were greater than the worldwide obesity rate. Determine if this group could be treated as a binomial distribution. State each requirement.

4) At Starbucks the advertised nutrition facts say that a Tall Chai latte with nonfat

milk has 32 grams of sugar, which is equivalent to 8 sugar cubes. Of course, there

will be some variability in sugar content. Suppose that the standard deviation is

about 0.1 grams. Engineers monitoring production processes assume that

measurements are normally distributed.

A quality control engineer randomly samples 10 Tall Chai Lattes and finds a

mean sugar content of32.07 grams. ls the difference between 32.07 and 32

statistically significant for a sample of 10?

a) Explain why we can use a normal curve to model the distribution of sample

means despite the fact that the samples only contain 10 lattes.

b) What is the z-score for the engineer's sample? What does the z-score tell us?

c) Is the sample statistically significant? Support your answer using probability.

students who participated in the​ study,

7878

correctly identified the color of the candy. The results are shown in the accompanying technology printout. Complete parts a through c below.

LOADING...

Click the icon to view the technology printout.

The proportion would be

0.50.5.

​(Type an integer or a​ decimal.)

b. Specify the null and alternative hypotheses for testing whether color and flavor are related. Choose the correct hypotheses below.

A.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p greater than 0.50H0: p=0.50 vs. Ha: p>0.50

B.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p less than 0.50H0: p=0.50 vs. Ha: p<0.50

C.

Upper H 0 : p not equals 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p≠0.50 vs. Ha: p=0.50

Your answer is not correct.

D.

Upper H 0 : p less than 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p<0.50 vs. Ha: p=0.50

E.

Upper H 0 : p equals 0.50 vs. Upper H Subscript a Baseline : p not equals 0.50H0: p=0.50 vs. Ha: p≠0.50

This is the correct answer.

F.

Upper H 0 : p greater than 0.50 vs. Upper H Subscript a Baseline : p equals 0.50H0: p>0.50 vs. Ha: p=0.50

c.

Carry out the test and give the appropriate conclusion at

alphaαequals=0.010.01.

Use the​ p-value of the​ test, shown on the accompanying technology​ printout, to make your decision.

The​ p-value is

0.0020.002.

​(Type an integer or a​ decimal.)

Make the appropriate conclusion using

alphaαequals=0.010.01.

A.

RejectReject

the null​ hypothesis, because the​ p-value is

not less thannot less than

alphaα.

There is

insufficientinsufficient

evidence to conclude that color and flavor are related.

B.

Do not rejectDo not reject

the null​ hypothesis, because the​ p-value is not

not less thannot less than

alpha

Cans of regular coke are labled to indicate they contain 12 oz. Lets say we have a sample n=36 with mean 12.19 oz. Assuming u=12oz and zigma=0.11oz, find the probablity that a sample of 36 cans will have a mean of 12.19 oz or greater. Do the results indicate an unusual event?

Suppose Canadian home-owners owe an average of $188,000 on their mortgages. Assume that mortgage debt is normally distributed in Canada with a standard deviation of $100,000.

Standard Normal Distribution Table

a. Albertans are reported to owe $242,000 in mortgage debt, much higher than the Canadian average. What is the probability of randomly selecting a Canadian with mortgage debt that exceeds $242,000?

Round to four decimal places if necessary

b. What is the probability of randomly selecting a Canadian with mortgage debt below $99,000?

Round to four decimal places if necessary

c. Determine the minimum mortgage debt owing by the 20% of Canadians with the largest mortgages.

Round to the nearest dollar

Anna suspected that when people exercise longer, their body temperatures change. She randomly assigned people to exercise for 30 or 60 minutes, then measured their temperatures. The 18 people who exercised for 30 minutes had a mean temperature of 38.3º C with a standard deviation of 0.27º C. The 24 people who exercised 60 minutes had a mean temperature of 38.9º C with a standard deviation of 0.29º C.

Assume Anna will use the conservative degrees of freedom from the smaller sample size.

Calculate the 90% confidence interval for the difference in mean body temperature after exercising for the two amounts of time.

What is the upper and lower limit?

In this assignment, you will learn how to describe the distribution of the sample mean (), and investigate how sample size affects variability of the sample mean (). To find out various probability values you will have to calculate the standard error of, and use the standard error to convert into Z score.

MARS Chocolate claims* that the net weight of its 31 oz Party Bucket is normally distributed with a mean of 32 oz and a standard deviation of 2 oz.

Assuming that the claim is correct, answer the following questions:

You must draw diagrams and show workings for questions (a) to (c).

(a) You purchase one of these Party Buckets, empty the content and measure its weight (denoted X). What is the chance that the weight (X) is less than 30 oz?

(b) Suppose you purchase 4 buckets and measure their mean weight ().

(i) Describe the probability distribution of the mean weight ().

(ii) What is the probability the mean weight () is less than 30 oz?

(c) Now suppose you purchase 9 buckets for a huge party and measure the mean weight ().

(i) Describe the probability distribution of the mean weight ().

(ii) What is the probability the mean weight () is less than 30 oz?

(d) Explain why your answer to (c)(ii) is different from (b)(ii).

According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets returned (BusinessWeek, January 15, 2007). A Houston department store sampled 80 items sold in January and found that 15 of the items were returned.

a) Construct a 90% confidence interval for the proportion of returns at the Houston store.

b) Is the proportion of returns at the Houston store significantly larger than the returns for the nation as a whole? Provide statistical support for your answer

Question 3 options:

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Let Z denote a standard normal random variable. Find the probability P(Z < 0.81)? The area to the LEFT of 0.81?

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Enter in format X.XX rounding UP so one-half (1/2) is 0.50 and two-thirds (2/3) is 0.67 with rounding. Enter -1.376 as -1.38 with rounding. NOTE: DO NOT ENTER A PERCENTAGE (%).

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Let Z denote a standard normal random variable. Find the probability P(Z > -1.29)? The area to the RIGHT of -1.29?

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Enter in format X.XX rounding UP so one-half (1/2) is 0.50 and two-thirds (2/3) is 0.67 with rounding. Enter -1.376 as -1.38 with rounding.  NOTE: DO NOT ENTER A PERCENTAGE (%).

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Let Z denote a standard normal random variable. Find the probability P(-1.70<Z<1.26)? The area BETWEEN -1.70 and 1.26?

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Enter in format X.XX rounding UP so one-half (1/2) is 0.50 and two-thirds (2/3) is 0.67 with rounding. Enter -1.376 as -1.38 with rounding. NOTE: DO NOT ENTER A PERCENTAGE (%).

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Let Z denote a standard normal random variable. Find the z-score for the 20th percentile?

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Enter in format X.XX rounding UP so one-half (1/2) is 0.50 and two-thirds (2/3) is 0.67 with rounding. Enter -1.376 as -1.38 with rounding.  NOTE: DO NOT ENTER A PERCENTAGE (%).

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Let Z denote a standard normal random variable. Find the z-score for with the area to the RIGHT equal to 0.32?

"Freshman 15": Fact or Fantasy? BOSTON Along with all of the typical "back-to-school" hype about lunch boxes and school buses, each September is typically greeted with media reports and advice about the "freshman 15," which is the popular name given to the phenomenon of first-year college students gaining 15 pounds during their freshman year. But does this 15 pound weight gain actually occur, or is it simply a myth? Carole Nhu'y Hodge, Linda Jackson, and Linda Sullivan are Michigan State University researchers who conducted their own investigation. They studied 61 Michigan State female students who took an introductory psychology course. The volunteers, who were given extra credit for participation in the experiment, were weighed at the beginning of their freshman year and at a point in time six month later. Among their findings reported in Psychology of Women Quarterly : "Body weight at the beginning of the first college year (Time 1) was compared with weight approximately 6 months later (Time 2). Average weight at Time 2, 131.45 lb (59.62 kg), was no different from average weight at Time 1, 130.57 lb (59.23 kg)." They also state that "Our findings suggest it (the 15-lb weight gain)is fantasy, although additional research is needed before drawing firm conclusions."

The Assignment:

Answer the following:

1. What do the researchers infer when they say that there is "no difference" between the mean weight at Time 1 (130.57 lb) and the mean weight at Time 2 (131.45lb), when there is an apparent difference of 0.88-lb?
2. What are the limitations of this particular study? That is, if the sample data are used to make inferences about a population, identify the specific population in question.
3. Identify any aspects of the experiment that could potentially threaten the validity of the results.
4. Identify a possible null hypothesis and alternative hypothesis for this experiment.
5. Your submission is to be a well-written grammatically correct response.

Sleep deprivation, CA vs. OR. For a recent report on sleep deprivation, the Centers for Disease Control and Prevention interviewed 11575 residents of California and 4783 residents of Oregon. In California, 903 respondents reported getting insufficient rest or sleep during each of the preceding 30 days, while 421 of the respondents from Oregon reported the same. Round each calculation to 4 decimal places.

1. Using California as population 1 and Oregon as population 2, what are the correct hypotheses for conducting a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states?

A. ?0:?1−?2=0H0:p1−p2=0, ??:?1−?2≠0HA:p1−p2≠0
B. ?0:?1−?2=0H0:p1−p2=0, ??:?1−?2>0HA:p1−p2>0
C. ?0:?1−?2=0H0:p1−p2=0, ??:?1−?2<0HA:p1−p2<0

2. Calculate the pooled estimate of the proportion for this test. ?̂p^ =

3. Calculate the standard error. SE =

4. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

5. Calculate the p-value for this hypothesis test. p-value =

6. Based on the p-value, we have:
A. very strong evidence
B. strong evidence
C. extremely strong evidence
D. little evidence
E. some evidence
that the null model is not a good fit for our observed data.

Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit seasonality, with the levels of pollutants showing patterns that vary over the hours in the day. On July 15, 16, and 17, the following levels of nitrogen dioxide were observed for the 12 hours from 6:00 A.M. to 6:00 P.M. (14 marks total)

July 15:

25

28

35

50

60

60

40

35

30

25

25

20

July 16:

28

30

35

48

60

65

50

40

35

25

20

20

July 17:

35

42

45

70

72

75

60

45

40

25

25

25

1. Construct a time series plot. What type of pattern exists in the data?

2. Use the following dummy variables to develop an estimated regression equation to account for the seasonal effects in the data.

Hour1=1 if the reading was made between 6:00 A.M. and 7:00 A.M.; Zero otherwise.

Hour2=1 if the reading was made between 7:00 A.M. and 8:00 A.M.; Zero otherwise.

Hour11=1 if the reading was made between 4:00 P.M. and 5:00 P.M.; Zero otherwise.

Note: that when the values of the 11 dummy variables are equal to zero, the observation corresponds to the 5:00 P.M. to 6:00 P.M. Hour.

c. Using the estimated regression equation developed in part (a), compute estimates of the levels of nitrogen dioxide for July 18.

d. Let t=1 to refer to the observation in hour 1 on July 15; t=2 to refer to the observation in hour 2 of July 15; ... and t=36 to refer to the observation in hour 12 of July 17. Using the dummy variables defined in part (b) and in t, develop an estimated regression equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute estimates of the levels of nitrogen dioxide for July 18.

Please show details of how to get answers in excel. Thanks!

2. The accountant at Superstore wants to determine the relationship between customer purchases at the store, Y ($), and the customer monthly salary, X ($). A sample of 15 customers is randomly selected and the results are summarized in the ANOVA table below:                                                                                                      15 Marks
df SS
Regression 1 176952
Residual 13 98236
Total 14    (A)

Coefficients Standard Error t Stat p-value
Intercept 78.58 7.540 1.202 0.035
Salary 0.066 0.013 4.948 0.003

a. Find A.
b. What is the estimated regression equation that relates the amount of customer’s purchase (Y) to the customer’s monthly salary (X)?
c.   Is the regression relationship significant? Use the p-value approach and 2% level of significance.
d.   Compute the coefficient of determination between the amount purchase and the customer’s monthly salary. Interpret the result in the context of the problem.

A child who gets into an elite preschool will have a lifetime earning potential given by a Poisson random variable with mean $3,310,000. If the child does not get into the preschool, her earning potential will be Poisson with mean $2,700,000. Let X = 1 if the child gets into the elite preschool, and zero otherwise, and assume that P(X = 1) = p.

(a) Find the covariance of X and the child’s lifetime earnings.

(b) Find the correlation of X and the child’s lifetime earnings.