Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 6.8 ppb arsenic, with s = 2.9 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ < 8 ppb; H₁: μ = 8 ppbH₀: μ = 8 ppb; H₁: μ < 8 ppb    H₀: μ = 8 ppb; H₁: μ ≠ 8 ppbH₀: μ = 8 ppb; H₁: μ > 8 ppbH₀: μ > 8 ppb; H₁: μ = 8 ppb

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since the sample size is large and σ is unknown.The standard normal, since the sample size is large and σ is known.    The Student's t, since the sample size is large and σ is known.The standard normal, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows.

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

(ii) Does this information indicate that the population average HC for this patient is higher than 14? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 14; H₁: μ ≠ 14H₀: μ = 14; H₁: μ < 14     H₀: μ < 14; H₁: μ = 14H₀: μ = 14; H₁: μ > 14H₀: μ > 14; H₁: μ = 14

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution and σ is unknown.The standard normal, since we assume that x has a normal distribution and σ is unknown.    The Student's t, since we assume that x has a normal distribution and σ is known.The standard normal, since we assume that x has a normal distribution and σ is known.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250    0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

Sketch the sampling distribution and show the area corresponding to the P-value.

he body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.21degrees°F

and a standard deviation of

0.66 degrees°F.

Using the empirical​ rule, find each approximate percentage below.

a. Approximately

what ​%

of healthy adults in this group have body temperatures within 1 standard deviation of the mean 97.55 and 98.87

11

standard

deviationdeviation

of the​ mean, or between

97.5597.55degrees°F

and

98.8798.87degrees°F.

​(Type an integer or a decimal. Do not​ round.)

he body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.2198.21degrees°F

and a standard deviation of

0.660.66degrees°F.

Using the empirical​ rule, find each approximate percentage below.

a. Approximately

nothing ​%

of healthy adults in this group have body temperatures within

11

standard

deviationdeviation

of the​ mean, or between

97.5597.55degrees°F

and

98.8798.87degrees°F.

​(Type an integer or a decimal. Do not​ round.)

he body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.2198.21degrees°F

and a standard deviation of

0.660.66degrees°F.

Using the empirical​ rule, find each approximate percentage below.

a. Approximately

nothing ​%

of healthy adults in this group have body temperatures within

11

standard

deviationdeviation

of the​ mean, or between

97.5597.55degrees°F

and

98.8798.87degrees°F.

​(Type an integer or a decimal. Do not​ round.)

he body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.2198.21degrees°F

and a standard deviation of

0.660.66degrees°F.

Using the empirical​ rule, find each approximate percentage below.

a. Approximately

nothing ​%

of healthy adults in this group have body temperatures within

11

standard

deviationdeviation

of the​ mean, or between

97.5597.55degrees°F

and

98.8798.87degrees°F.

​(Type an integer or a decimal. Do not​ round.)

he body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of

98.2198.21degrees°F

and a standard deviation of

0.660.66degrees°F.

Using the empirical​ rule, find each approximate percentage below.

a. Approximately

nothing ​%

of healthy adults in this group have body temperatures within

11

standard

deviation

of the​ mean, or between

97.55.55degrees°F

and

98.87 degrees°F.

​(Type an integer or a decimal. Do not​ round.)

) Ben and Allison each decide to wager 1 unit against the other person on flips
of an unfair coin, with probability 0.6 of landing head, until one of them runs out of money.
When the flip lands on head, Ben wins 1 unit from Allison; and when the coin lands on tail,
Allison wins 1 from Ben. At the start of the contest, Ben has 30 units and Allison has 45
units. Find
(a) the average number of flips needed until Ben is eventually broke,
(b) the average number of flips needed until Allison is eventually broke, and
(c) the average number of flips needed until either Ben or Allison is eventually broke.

13. A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with its new local community and has encouraged its professional employees to engage in local service activities. The company believes that its professionals volunteer an average of more than 15 hours per month. If this is not the case, it will institute an incentive program to increase community involvement.

(a) A random sample of 24 professionals reported the sample mean and standard deviation are 16.6 hours and 2.22 hours respectively. For a more accurate determination, top management wants to estimate the average number of hours volunteered per month by their professional staff to within half an hour with 99% confidence. How many randomly selected professional employees would they need to sample?

(b) Now, suppose 40 professional employees are randomly selected. This sample yields a mean of 15.2 hours and a standard deviation of 1.8 hours. Construct the 95% confidence interval. (Hint: 1.8 is the sample standard deviation, not the population standard deviation)

Question 1: A mobile phone manufacturer claims that the batteries in the manufactured mobile phones are used for an average of 140 hours after being charged once. For this purpose, 17 telephone batteries were chosen randomly and it was determined that they could be used for an average of 136 hours and the standard deviation was 29 hours. According to this;

a-) Is the batteries lasting less than 140 minutes according to 1% significance level? Examine statistically.

b-) Determine the confidence interval of the batteries' standby time at 1% significance level.

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is estimated that 3.5% of the general population will live past their 90th birthday. In a graduating class of 759 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday


(b) 30 or more will live beyond their 90th birthday


(c) between 25 and 35 will live beyond their 90th birthday


(d) more than 40 will live beyond their 90th birthday

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 47% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 27 strikes. Find the following probabilities. (Round your answers to four decimal places.)

ASK YOUR TEACHER

Based on long experience, an airline found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 263 ticket reservations for an airplane with only 255 seats.(a) What is the probability that a person holding a reservation will show up for the flight?


(b) Let n = 263 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. What expression represents the probability that a seat will be available for everyone who shows up holding a reservation?

P(r ≥ 263)P(r ≤ 263)    P(r ≥ 255)P(r ≤ 255

(c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)

One environmental group did a study of recycling habits in a California community. It found that 74% of the aluminum cans sold in the area were recycled. (Use the normal approximation. Round your answers to four decimal places.)

(a) If 384 cans are sold today, what is the probability that 300 or more will be recycled?


(b) Of the 384 cans sold, what is the probability that between 260 and 300 will be recycled?

Let X has the probability density function (pdf)

f(x)={C1, if 0 < x ≤ 1,

C2x, if1<x≤4,

0, otherwise.

Assume that the mean E(X) = 2.57.

(a) Find the normalizing constants C1 and C2.

(b) Find the cdf of X, FX.

(c) Find the variance Var(X) and the 0.28 quantile q0.28 of X.

(d)LetY =kX. Find all constants k such that Pr(1<Y <9)=0.035. Hint: express the event {1 < Y < 9} in terms of the random variable X and then use the cdf of X, FX.

Consider a regression model Y_i=β₀₊β₁X_i+u_i and suppose from a sample of 10 observations you are provided the following information:

∑10i=1Yi=71;  ∑10i=1Xi=42;  ∑10i=1XiYi=308; ∑10i=1X2i=196

Given this information, what is the predicted value of Y, i.e.,Yˆ for x = 12?

1. 14

2. 11

3. 13

4. 12

5. 15

Case 7.2

Skyhigh Airlines

Skyhigh Airlines flight 708 from New York to Los Angeles is a popular flight that is

usually sold out. Unfortunately, some ticketed passengers change their plans at the last

minute and cancel or re-book on another flight. Subsequently, the airline loses the $450

for every empty seat that the plane flies.

To limit their losses from no-shows, the airline routinely overbooks flight 708, and hopes

that the number of no-shows will equal the number of seats oversold. However, things

seldom work out that well. Sometimes flight 708 has empty seats, and other times there

are more passengers than the airplane has seats. When the latter happens, the airline must

“bump” pre-ticketed passengers; they estimate that this will cost them $275 in later

accommodations to bumped passengers.

Fortunately for the airline, hopeful passengers usually show up at flight time without

tickets and want to get on the flight. The airline classifies these passengers as standbys

while it waits to determine how many seats, if any will be available. Standby passengers

can help offset the loss associated with flying an empty seat, but the airline suffers no

penalty when a standby passenger is not able to receive a seat.

Airline records indicate that the number of No-shows and Standbys will vary according

to the probability tables below: (see bottom of page)

Simulate 25 flights with each of several different overbooking decisions (assume that the

best overbooking number will be between 1 and 6) to determine the optimal number of

seats to overbook this flight, to minimize the airline’s losses. Tabulate your results and

use them to justify your recommendations. You should report, for each scenario, the

average loss per flight, and the percentage of flights that suffer a loss.

6. Enthalpy is a measure of total energy in a thermodynamic system. The following table presents enthalpy measurements on 16 water based systems. Four measurements are made on each of four systems which differ by concentration of NaCl (table salt).

3. What pairs of concentrations, if any, can you conclude to have differing enthalpies? Use α = 0.05.

All concentrations are significant at the 0.05 level. WHY?

4. Compute the quantity s = (MSE)^0.5, the estimate of the standard deviation σ.

5. Assuming s to be the error standard deviation, find the sample size necessary in each treatment to provide a power of 0.80 to detect a maximum difference of 0.1 in the treatment means at the 5% level.

The purpose of this assignment is to apply a waiting line model to a business service operation in order to recommend the most efficient use of time and resources. (This assignment has been adapted from Case Problem 2 in Chapter 15 of the textbook.) Use the information in the scenario provided to prepare a managerial report for Office Equipment, Inc. (OEI). Scenario Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of 3 hours from the time that the customer notifies OEI of an equipment problem. Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates that a customer requests a service call at an average rate of one call per 50 hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer’s office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a new customer calls for service, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, after the technician is free from all existing service commitments, the technician takes an average of 1 hour of travel time to reach the new customer’s office and an average of 1.5 hours to complete the repair service. The cost of the service technician is $80 per hour. The downtime cost (wait time and service time) for customers is $100 per hour. OEI is planning to expand its business. Within 1 year, OEI projects that it will have 20 customers, and within 2 years, OEI projects that it will have 30 customers. Although OEI is satisfied that one service technician can handle the 10 existing customers, management is concerned about the ability of one technician to meet the average 3-hour service call guarantee when the OEI customer base expands. In a recent planning meeting, the marketing manager made a proposal to add a second service technician when OEI reaches 20 customers and to add a third service technician when OEI reaches 30 customers. Before making a final decision, management would like an analysis of OEI service capabilities. OEI is particularly interested in meeting the average 3-hour waiting time guarantee at the lowest possible total cost. Managerial Report Develop a managerial report (1,000-1,250 words) summarizing your analysis of the OEI service capabilities. Make recommendations regarding the number of technicians to be used when OEI reaches 20 and then 30 customers, and justify your response. Include a discussion of the following issues in your report: 4. OEI is satisfied that one service technician can handle the 10 existing customers. Use a waiting line model to determine the following information: (a) probability that no customers are in the system, (b) average number of customers in the waiting line, (c) average number of customers in the system, (d) average time a customer waits until the service technician arrives, (e) average time a customer waits until the machine is back in operation, (f) probability that a customer will have to wait more than one hour for the service technician to arrive, and (g) the total cost per hour for the service operation. I need help with this part, please show all your work.

Linear regression

Hello

What does it mean that the residuals in linear regression is normal distributed? Why is it only the residuals that is, and not the "raw" data? And why do we want our residuals to be normal?

Explain the concept and purpose of z-scores and calculate them for the performance of the following set of portfolio managers.