You randomly select 20 coffee shops and measure the temperature of the coffee sold at each. The sample mean temperature is 162.0ºF with a sample standard deviation of 10.0ºF. Assume the temperatures are approximately normally distributed. Find the test statistic to test if population average temperature of the coffee is different than 163.5 F.

Solve using R

Either copy & paste each answer from your data sheet, or round your answers to two decimal places where applicable.

Mean

Standard Error

Median

Mode  (report #N/A if no mode)

Standard Deviation

Sample Variance

Kurtosis

Skewness

Range

Minimum/smallest

Maximum/Largest

Sum

Count

Did you notice the mistake in the video while using the data analysis tool? The data range to B1:B100 was selected instead of B1:B101 so there were only 99 values for the Count when the data analysis tool ran. Be sure not to make the same mistake.

The NBS television network earns an average of $400,000 from a hit show and loses an average

of $100,000 on a flop. Of all shows reviewed by the network, 25% turn out to be hits and 75%

turn out to be flops. For $40,000, a market research firm will have an audience view a pilot of a

prospective show and give its view about whether a show will be a hit or a flop. If a show is

actually going to be a hit, there is a 90% chance that the market research firm will predict the

show to be a hit. If the show is actually going to be a flop, there is an 80% chance that the

market research firm will predict the show to be a flop. Determine how the network can

maximize its expected profits by doing the following:

a. Construct the decision tree.

b. What would be the expected profit if the market research firm is hired?

A. According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question. At least 3 flights are not on time.

B. According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question. At the most 8 flights are on time.

c. According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question. In between 6 and 9 flights are on time.

Consider the following all-integer linear program:

1. Solve the LP Relaxation of this problem.
   The optimal solution to the LP Relaxation is x₁ = ___, x₂ = .____________
   
   Its value is ___________
2. Find the optimal integer solution.
   The optimal solution to the LP Relaxation is x₁ = _____x₂ = __________
   Its value is _______

A steel company is considering the relocation of one of its manufacturing plants. The company’s executives have selected four areas that they believe are suitable locations. However, they want to determine if the average wages are significantly different in any of the locations, since this could have a major impact on the cost of production. A survey of hourly wages of similar workers in each of the four areas I performed with the following results.

a. Do the data indicate a significant difference among the average hourly wages in the four areas? Construct the 10 steps of hypothesis testing using α = 0.05 to answer the question.

b. What assumptions were mad in performing the test in part a? Do the data appear to satisfy these assumptions? Explain.

Problem 2: (Revised 6.3) Magazine Advertising: In a study of revenue from advertising, data were collected for 41 magazines list as follows. The variables observed are number of pages of advertising and advertising revenue. The names of the magazines are listed as:

Here is the code help you to paste data into your R:

data6<-'Adv Revenue
25 50
15 49.7
20 34
17 30.7
23 27
17 26.3
14 24.6
22 16.9
12 16.7
15 14.6
8 13.8
7 13.2
9 13.1
12 10.6
1 8.8
6 8.7
12 8.5
9 8.3
7 8.2
9 8.2
7 7.3
1 7
77 6.6
13 6.2
5 5.8
7 5.1
13 4.1
4 3.9
6 3.9
3 3.5
6 3.3
4 3
3 2.5
3 2.3
5 2.3
4 1.8
4 1.5
3 1.3
3 1.3
4 1
2 0.3
'
data6n<-read.table(textConnection(object=data6),
header=TRUE,
sep="",
stringsAsFactors = FALSE)

a. You should not be surprised by the presence of a large number of outliers because the magazines are highly heterogeneous and it is unrealistic to expect a single relationship to connect all of them. Find outliers and high leverage points. Delete the outliers and obtain an acceptable regression equation that relates advertising revenue to advertising pages.

b. For the deleted data, check the homogeneity of the variance. Choose an appropriate transformation of the data and fit the model to the transformed data. Evaluate the fit.

Use R.  Provide Solution and R Code within each problem.

A study was conducted to determine the average weight of newborn babies. The distribution of the weight of newborn babies has a standard deviation of σ = 1.25lbs. A random sample of 100 newborn babies was taken and weights measured. The mean weight of the babies in the sample was 7.3 lbs.

a. Construct a 95% confidence interval for the true mean weight of newborn babies.

b. Interpret the confidence interval in a.

c. Write the null and alternative hypotheses to determine if the true mean weight of newborn babies is less than 7.75 lbs.

d. Conduct a statistical test to determine if the true mean weight of newborn babies is less than 7.75 lbs.

i. Pvalue

ii. Conclusion

> fm1 <- lm(ascorbic ~ pct.dry + cultB.id + cultC.id, data=lima)

> summary(fm1)

Coefficients: Estimate Std. Error t value Pr(>|t|)

(Intercept) 213.2 16.3 13.1 4.64e-08 ***

pct.dry    -3.9 0.43 -9.1 1.96e-06 ***

cultB.id -6.2 5.53 -1.1 0.290

cultC.id    20.5 5.42 3.8 0.003 **

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

Residual standard error: -- intentionally omitted -Multiple R-squared: 0.91, Adjusted R-squared: 0.88 F-statistic: 36.84 on 3 and 11 DF, p-value: 4.956e-06

(c) Determine whether each of the statements below is supported by the multiple regression model above. If the statement is supported, circle “yes”. If the statement is not supported, circle “no”.
YES NO (i) After controlling for differences among the cultivars, there is strong evidence that ascorbic acid content decreases as percent dry weight increases.
YES NO (ii) The estimate of the intercept suggests that lima bean plans of cultivar A have an average ascorbic acid content of 213.
YES NO (iii) After accounting for the effect of percent dry weight, there is strong evidence that the ascorbic acid content of cultivar B is less than the ascorbic acid content of cultivar A.
YES NO (iv) After accounting for the effect of percent dry weight, there is strong evidence that the ascorbic acid content of cultivar C is less than the ascorbic acid content of cultivar A.

The drive-thru times at Tim Horton’s are normally distributed with µ = 138.5 seconds and σ = 29 seconds.

(a) What is the probability that a randomly selected car will get through the drive-thru in less than 100 seconds?

(b) What is the probability that a randomly selected car will spend more than 160 seconds in the drive-thru?

(c) What proportion of cars spend between 2 and 3 minutes in the drive-thru?

(d) Would it be unusual for a car to spend more than 3 minutes in the drive-thru? Why?

The City of Charlotte is experiencing flooding. The City has determined that it will activate the flood

gates when the average flood level reaches 2 feet. The flood control system is activated and

resources are directed to flood control when the flood condition is equal to or more than the 2 feet

standard the City has set. The City sampled 20 spots in the urban area between 7:00am and 8:00am.

This data set will be posted to Canvas. Examine the data using the concepts you have learned in

Chapter 10. Should the City activate the flood control system? Why or why not?

Data Set:

Areas. Feet of Flood Water

1 0

2 3

3 1

4 2

5 0

6 0

7 2

8 3

9 1

10 3

11 2

12 2

13 5

14 1

15 2

16 0

17 2

18 1

19 0

20 2

8. Suppose 22% of the eggs sold at a local grocery store that are graded “large” are smaller than that and should be graded “medium.” A random sample of 15 eggs graded large is obtained. Answer the following using the binomial distribution:(Round to 4 (FOUR) decimal places.)

What is the probability that 8 or more of the “large” eggs sampled are really medium-sized?

What is the probability fewer than 3 of the “large” eggs sampled are really medium-sized?

What is the probability that none of the “large” eggs sampled are really medium-sized?

What is the probability that exactly 4 of the “large” eggs sampled are really medium-sized?

What is the probability that all of the “large” eggs sampled are really medium-sized?

What is the probability that 6 or 7 of the “large” eggs sampled are really medium-sized?

The ages of commercial aircraft are normally distributed with a mean of 13.5 years and a standard deviation of 8.2933 years. What percentage of individual aircraft have ages between 10 years and 16 ​years? Assume that a random sample of 81 aircraft is selected and the mean age of the sample is computed. What percentage of sample means have ages between 10 years and 16 years?

The Perotti Pharma Company is investigating the relationship between advertising expenditures and the sales of some over-the-counter (OTC) drugs.

The following data represents a sample of 10 common OTC drugs. Note that AD = Advertising dollars in millions and S = Sales in millions $.

1. What is the equation of the regression line?

2. Interpret the slope in the context of the problem.

3. Find the coefficient of determination.

4. Interpret the meaning of R² in the context of the problem.

5. State the hypotheses to test for the significance of the regression equation.

6. Is there a significant relationship between dependent and independent variables at alpha=0.05? Why?

7. Create a 95% confidence interval for Sales if Advertising dollars = $50 million and interpret its meaning.

8. Paste the table with the results of regression analysis.