1. If the number of arrivals at a cell phone kiosk has a rate of 0.80 customers per hour.

to. What is the probability that less than 2 clients arrive in the next half hour? (10 points)

b. What is the probability that in the next three hours between 2 and 4 clients will arrive inclusive? (10 points)

c. Last customer arrived at 2:00 pm, what is the probability that the next customer takes more than 60 minutes to arrive? (10 points)

d. What is the average time between arrivals in minutes? (5 points)

and. What is the medina of the time between arrivals? (5 points)

F. What is the 80% percentile? (5 points)

. A researcher wishes to see if the mean number of days that a basic, low-price, small automobile sits on a dealer’s lot is 29. A sample of 30 automobile dealers has a mean of 30.1 days for this type of automobile. At an alpha 0f 0.05, test the claim that the meantime is greater than 29 days. The standard deviation (sigma) of the population is 3.8 days.

a. Support the claim b. Do not support the claim

. It has been reported that the average credit card debt for college seniors at the college book store at a college or univerisity is 3262 dollars. The student senate at a large university feels that their seniors have a debt much less than this, so it conducts a study of 50 randomly selected seniors and find that the average debt is 2995 dollars. The population standard deviation (sigma) is 1100 dollars. With an alpha of 0.05, is the student senate correct?

a. Yes b. No

12.25 Mendel formulated the law of independent assortment as his second law of inheritance. It involves two genes independently segregated during reproduction, each independently determining one aspect of the phenotype. In one experiment, Mendel crossed pea plants producing yellow, round seeds with pea plants producing green, wrinkled seeds. The first generation resulted in only plants producing yellow, round seeds. Self-crossing of the F1 yielded the following phenotypes in F2: Assuming two independent genes, each with a dominant and a recessive alleles, we would expect to find a 9:3:3:1 phenotypic ratio.

a) Are the conditions for a chi-square goodness of fit test satisfied?

b) What are the null and alternative hypotheses for this test?

c) What are the expected counts under the null hypothesis? Phenotype Y Round Y wrinkled G Round G Wrinkled Observed Expected

d)

The chi-square statistic for this test is χ2 = 0.47. Use Table D to find the P-value. What can you conclude? Do the data agree with Mendel’s second law of genetic inheritance?

Group1: [4,5,3,4,5,5,2]

Group2:[3,4,5,2,3,1,1,2]

Group3:[1,1,1,2,1,3]

Perform a Kruskal-Wallis test, calculate test statistic, find p-value by chi-square approximation, and state you conclusion

The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.

a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)

taxes = ______ + ______ size

b. Interpret the slope coefficient.

a. As Property Taxes increase by 1 dollar, the size of the house increases by 6.78 ft.

b. As Size increases by 1 square foot, the property taxes are predicted to increase by $6.78.

c. Predict the property taxes for a 1,500-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

taxes _________

Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.)

(a)At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?

What is the probability that 5 or more are extroverts?

What is the probability that all are extroverts?

(b) In a group of 5 computer programmers, what is the probability that none are introverts?

What is the probability that 3 or more are introverts?   

is the probability that all are introverts?

Please provide explanation and right answer

A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City. [You may find it useful to reference the t table.]

a-1. Calculate the sample correlation coefficient r_xy. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

a-2. Interpret r_xy.

a. The correlation coefficient indicates a positive linear relationship.

b. The correlation coefficient indicates a negative linear relationship.

c. The correlation coefficient indicates no linear relationship.

b. Specify the competing hypotheses in order to determine whether the population correlation coefficient between the size of a house and property taxes differs from zero.

a. H₀: ρ_xy = 0; H_A: ρ_xy ≠ 0

b. H₀: ρ_xy ≥ 0; H_A: ρ_xy < 0

c. H₀: ρ_xy ≤ 0; H_A: ρ_xy > 0

c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c-2. Find the p-value.

a. p-value < 0.01

b. p-value  0.10

c. 0.05  p-value < 0.10

d. 0.02  p-value < 0.05

e. 0.01  p-value < 0.02

d. At the 5% significance level, what is the conclusion to the test?

a. Reject H₀; we can state size and property taxes are correlated.

b. Reject H₀; we cannot state size and property taxes are correlated.

c. Do not reject H₀; we can state size and property taxes are correlated.

d. Do not reject H₀; we cannot state size and property taxes are correlated.

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 3 decimal places.)

Salary= (blank) +(blank)Education

b. Interpret the coefficient for Education.

a. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $7,161.

b. As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

c. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

d. As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $7,161.

c. What is the predicted salary for an individual who completed 6 years of higher education? (Round answer to the nearest whole number.)

A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City.

a-1. Calculate the sample correlation coefficient r_xy. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

a-2. Interpret r_xy.

a. The correlation coefficient indicates a positive linear relationship.

b. The correlation coefficient indicates a negative linear relationship.

c. The correlation coefficient indicates no linear relationship.

b. Specify the competing hypotheses in order to determine whether the population correlation coefficient between the size of a house and property taxes differs from zero.

a. H₀: ρ_xy = 0; H_A: ρ_xy ≠ 0

b. H₀: ρ_xy ≥ 0; H_A: ρ_xy < 0

c. H₀: ρ_xy ≤ 0; H_A: ρ_xy > 0

c-1. Calculate the value of the test statistic.

c-2. Find the p-value.

a. p-value < 0.01

b. p-value  0.10

c. 0.05  p-value < 0.10

d. 0.02  p-value < 0.05

e. 0.01  p-value < 0.02

d. At the 1% significance level, what is the conclusion to the test?

a. Reject H₀; we can state size and property taxes are correlated.

b. Reject H₀; we cannot state size and property taxes are correlated.

c. Do not reject H₀; we can state size and property taxes are correlated.

d. Do not reject H₀; we cannot state size and property taxes are correlated.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

Listed below are ages of actresses and actors from a country at the times that they won a certain award. The data are paired according to the years that they won. Use a 0.01 significance level to test the belief that best actresses are younger than best actors. Does the result suggest a problem in that culture? Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal.

Best Actresses 33 29 27 27 37 41 28 38 26 21 33 42 32 30 35

Best Actors 30 41 48 52 40 39 62 34 34 62 42 56 41 33 29

The following data presents the number of units of production per day turnout by 5 different number of workers using five different number of machines.
                 Machines types
Workers A     B   C    D
1.            44   38 47 36
2.            46 40 52 43
3.            34 36 44 32
4.           43 38 46 33
5.            38 42 49 39
1. test whether the mean productivity is same for the different machines

2. test whether the five workers differ with respect to
mean productivity

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $34 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 50 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the xdistribution?

The sampling distribution of x is approximately normal with mean μ_x = 34 and standard error σ_x = $0.99.The sampling distribution of x is approximately normal with mean μ_x = 34 and standard error σ_x = $7.     The sampling distribution of x is approximately normal with mean μ_x = 34 and standard error σ_x = $0.14.The sampling distribution of x is not normal.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is not necessary to make any assumption about the x distribution because n is large.It is not necessary to make any assumption about the x distribution because μ is large.     It is necessary to assume that x has a large distribution.It is necessary to assume that x has an approximately normal distribution.

(b) What is the probability that x is between $32 and $36? (Round your answer to four decimal places.)


(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $32 and $36? (Round your answer to four decimal places.)


(d) In part (b), we used x, the average amount spent, computed for 50 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The standard deviation is larger for the x distribution than it is for the x distribution.The x distribution is approximately normal while the x distribution is not normal.     The standard deviation is smaller for the x distribution than it is for the x distribution.The sample size is smaller for the x distribution than it is for the x distribution.The mean is larger for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.     

How much does a sleeping bag cost? Let’s say you want a sleeping bag that should keep you warm in temperatures from 20oF to 45oF. A random sample of prices ($) for sleeping bags in this temperature range was taken from Backpacker Magazine: Gear Guide (Vol. 25, Issue 157, No. 2.)

80      90        100      120      75      37      30        23        100      100

105      95        105      60      110      120      95        90        60        70

Find the mean x ( round to two decimals places)

Find the sample standard deviation   s    ( round to two decimals places)

Find a 90% confidence interval for the mean price µ of all summer sleeping bags.

2. Over the past few months, an adult patient has been treated for tetany (severe muscle spasms.) This condition is associated with total calcium level below 6 mg/dl . Reference: Manual of Laboratory and Diagnostics Tests by F. Fischbach). Recently, the patient’s total calcium tests gave the following readings in mg/dl

9.3       8.8       10.1     8.9       9.4       9.8

10.0     9.9       11.2     12.1

Find the mean x      ( round to two decimals places)

Find the sample standard deviation   s     (round to two decimals places)

Find a 99.9% confidence interval for the mean calcium level.

3.A random sample of 40 students taken from a university showed that their mean GPA is 2.94 and the standard deviation of their GPAs is .30. Construct a 99% confidence interval for the mean GPA of all students at this university.

4.According to a study done by Dr. Martha S. Linet and others, the mean duration of the most recent headache was 8.2 hours for a sample of 5055 females 12 through 29. Make a 95% confidence interval for the mean duration of all headaches for all 12 to 29-year-old females. The standard deviation for this sample is 2.4 hours.

5. According to a survey conducted by USA TODAY, 73.2% of the workers in the United States drive alone to work. Assume that this survey is based on a random sample of 1000 US workers.

Find a 95% confidence interval for all workers in the United States who drive alone to work.

We when run a hypothesis test, we are looking to verify a claim about a population parameter. Why is it important that we have a statistical tool to allow us to do this? For example, suppose that you were the quality control officer for a CPU manufacturer. Your job is to ensure that the CPUs your company makes meet certain performance standards so that when they are installed in iPhones they function properly and the phone company can truthfully claim that its phone will perform in certain ways. What would you do to verify that your CPUs were meeting both industry standards as well as the expectations of those companies that will purchase them for use in their products?