A) Test these hypothesis by calculating the p value given that xbar=99, n=100, and standard deviation =8.

Ho: mu=100

H1: mu does not equal 100

B) repeat part a with n=50

C) repeat part a with n=20 D) what is the effect on the value of the test statistic and the p value of the test when the sample size decreases?

PLEASE DO NOT USE MINITAB. YOU MAY USE EXCEL OR DO IT MANUALLY.

Supposed you were asked to estimate the proportion of 25-30 year olds that have a home (land line) telephone. In order to make this estimate, you polled 600 people in this age range and the bellows were reported below: [25] pts. Total]

            Home Phone              Frequency

            NO                                    450

            YES                                  150

                                                        600

1. What is the proportion of the sample that report YES, they have a home phone line? [5 pts]

2. What condition must be met in order to calculate a confidence interval to estimate this proportion? Is this condition met? [5 pts.]

3. Develop a 95% confidence interval for the proportion of all of 25-30 year olds that have a home (land line) telephone

In stratified sampling, there are two methods of sample size allocation to the strata: optimal allocation and proportional-to-size allocation. Suppose interest lies in estimating the mean of the population using ŭstrat(y). Let Vopt show the variance of ŭstrat(y) under optional allocation and Vprop show the variance of ŭstrat(y) under proportional-to-size allocation.

(a) [4 marks] Show, with detailed steps, that Vopt <= Vprop.

(b) [2 marks] under what conditions Vopt = Vprop? provide a proof for your answer.

A PEW POLL TAKEN IN 2010 SURVEYED 830 PEOPLE AGED 18-29, AND FOUND THAT 166 OF
They HAD ONE OR MORE TATTOOS. CAN YOU CONCLUDE THAT THE PERCENTAGE OF PEOPLE
AGED 18-29 WHO HAS A TATTOO IS LESS THAN 25%.

a) WRITE THE HYPOTHESIS TEST.

b) WHAT KIND OF TEST IS IT?

c) WHAT IS THE SAMPLE MEAN?

d) FIND THE STANDARD ERROR.

e) DRAW THE BELL CURVE RELATIVE TO H 0

f) FIND THE Z STAT FOR THE SAMPLE MEAN THAT YOU FOUND IN (C)

g) DRAW THE P-VALUE REGION ON THE STANDARD BELL

h) FIND THE P-VALUE

i) WHAT IS THE RESULT AT α = 0.01?

j) WRITE A SENTENCE ABOUT THE RESULT WITH RESPECT

Dear Math Students:

I recently bought a restaurant in Chicago.  It is pretty small, but well-located.  We are open every day, but Mondays, from 4 PM until 11 PM.  Our menu is basically Italian.  We offer individual pizzas, pastas, salads, and a special of the day. We also have really good desserts. We offer cookies, ice cream and superb cakes.  Last month we had 800 customers.  Our salads are considered a whole meal, so people don’t usually order another entrée with them.  Last month, we sold 400 pizzas, 200 pasta dishes, 130 salads, and 70 specials of the day. Not everyone orders a dessert, but last month we sold 200 cookies, 100 ice creams, and 250 cakes.  Next week we are expecting 250 to 300 customers.  I need to know how many of each of the entrees and how many of each of the desserts I can expect to sell.

I would also like to know how much money I can expect to make.  Perhaps you could also let me know how much the average customer spends. Let me tell you the prices.  The pizzas are $7.95.  The pastas are sold for $8.95.  The salads are $6.95.  The special of the day is $9.95.  As for the desserts, the cookies are $1.00, the ice cream is $1.50, and the cakes are $3.00

Thanks a lot for your help, I am not very good at math, but perhaps you could try to explain your answers in such a way that I could estimate them for myself next time.

Yours sincerely,

Chris Smith

Pizza Plus

`~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Put the results of your calculations here and the explanation of your calculations o the back of this sheet.

Estimates for 250 customers

Average customer spends: $________________

Estimates for 300 customers

Average customer spends: $________________

Explanation of Calculations:

Teenager Mike wants to borrow the car. He can ask either parent for permission to take the car. If he asks his mom, there is a 20% chance she will say ”yes,” a 30% chance she will say ”no,” and a 50% chance she will say, ”ask your father.” Similarly, that chances of hearing ”yes”/”no”/”ask your mother” from his dad are 0.1, 0.2, and 0.7 respectively. Imagine Mike’s efforts can be modeled as a Markov chain with state (1) talk to Mom, (2) talk to Dad, (3) get the car (”yes”), (4) strike out (”no”). Assume that once either parent has said ”yes” or ”no,” Mike’s begging is done.

1. Construct the one-step transition matrix for this Markov chain.

2. Identify the absorbing state(s) of the chain.

3. Determine the mean times to absorption.

4. Determine the probability that Mike will eventually get the car if (1) he asks Mom fist and (2) he asks Dad first. Whom should he ask first?

Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.

Give the 95^th Percentile. (Round your answer to two decimal places.)

Reserve Problems Chapter 8 Section 2 Problem 2

During the nutrition research, the amount of consumed kilocalories per day was measured for 18 people – 10 women and 8 men. Results are as follows:

Women: 1962, 1842, 1588, 1911, 1779, 1603, 1758, 1771, 1874, 1974;

Men: 2097, 2560, 2328, 2399, 2420, 2292, 2263, 2047.

Calculate a 90% confidence interval on the mean for women and men separately. Assume distribution to be normal.
Round your answers to the nearest integer (e.g. 9876).

Let XiXi for i=1,2,3,…i=1,2,3,… be a random variable whose probability distribution is Poisson with parameter λ=9λ=9. Assume the Xi are independent. Note that Poisson distributions are discrete.

Let Sn=X1+⋯+Xn.

To use a Normal distribution to approximate P(550≤S64≤600), we use the area from a lower bound of __ to an upper bound of __ under a Normal curve with center (average) at __ and spread (standard deviation) of __ .

The estimated probability is __

A grocery store is trying to predict how many packages of toilet paper rolls will be purchased over the next week. They know from their records that each customer has a 60% chance of buying 0 packages, a 30% chance of buying 1 package, an 8% chance of buying 2, and a 2% chance of buying 25. They expect about 150 customers per day.

What is the probability that the average number of packages per customer is greater than 1 over the course of a week? Assume the store is open 7 days a week.

Please calculate the standard error.

The number of errors in each of 300 files has a Poisson distribution with 1.4 errors per file on average. Assume the errors in different files are independent. Use the Central Limit Theorem to approximate the probability that the total number of errors is at least 400. (Use a calculator.)

) In a study of the effects of caffeine on alertness, 32 subjects were randomly assigned to four groups. These groups were C1: wait-list control (no treatment), C2: placebo control, E1: experimental group 1 (mild caffeine treatment) and E2: experimental groups 2 (high caffeine treatment). Several subjects were not able to complete the study, reducing the group n’s to 7, 5, 6, and 3, respectively. The dependent variable scores were performance scores on a visual-motor task requiring alertness. The results are as follows:

Do the results indicate a significant difference between treatment groups? State the null hypothesis, Fcritical, η2, and use Scheffe’s test to determine which treatment conditions differ in the event of rejecting the null hypothesis. Conclude with a summary appropriate for publication.

A marketing company wants to know the mean price of new vehicles sold in an up-and‑coming area of town. Marketing strategists takes a simple random sample of 756 cars, and find that the sample has a mean of $27,400 and a standard deviation of $1300.

1. Assume that the population standard deviation is unknown. What is the error of estimate for a 95% confidence interval?

2. Assume that the population standard deviation is known to be $1500. What is the upper bound for a 98% confidence interval?

3. Assume that the population standard deviation is known to be $1500. Find the error of estimate for a 99% confidence interval.

4. Assume that the population standard deviation is known. If the marketing strategists want the 90% confidence interval to be within $50 of the population mean, how many cars at minimum should they sample?

The average undergraduate cost of tuition, fees and books for a two year college is $10,560. Four years later, a random sample 36 two year colleges, had an average cost of tuition, fees and books of $11,380 and a standard deviation of $1300, with a normal distribution. At α = 2%, has the average cost of two-year college increased?

1) Check and state the conditions for statistical inference.

2) Compute a 95% confidence interval for the average cost of tuition fees and books for a two year college.

3) Write a statement interpreting the confidence interval.

4) Write the null and alternate hypotheses.

5) Calculate the standard error and sketch the model, marking the center and ± SD’s

6) Calculate the p-value, showing ALL the work.

7) State the conclusion, remember there are three parts. Remember that α =2% or α =.02.

Some of the statements below refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p).

A. The mean number of years Americans work before retiring is 34. (out of the following)

H₀: p = 34,     H_a: p ≠ 34

H₀: μ = 34,     H_a: μ ≠ 34     

H₀: p ≥ 34,     H_a: p < 34

H₀: p ≤ 34,     H_a: p > 34

H₀: μ ≤ 34,     H_a: μ > 34

H₀: μ ≠ 34,     H_a: μ = 34

H₀: μ ≥ 34,     H_a: μ < 34

H₀: p ≠ 34,     H_a: p = 34

B. At most 60% of Americans vote in presidential elections. (Out of the following)

H₀: p ≤ 0.60,     H_a: p > 0.60

H₀: p > 0.60,     H_a: p ≤ 0.60     

H₀: p = 0.60,     H_a: p > 0.60

H₀: μ = 60,     H_a: μ > 60

H₀: μ < 60,     H_a: μ > 60

H₀: μ > 60,     H_a: μ ≤ 60

H₀: p < 0.60,     H_a: p > 0.60

H₀: μ ≤ 60,     H_a: μ > 60

C. The mean starting salary for San Jose State University graduates is at least $100,000 per year. (out of the following)

H₀: p = 100,000,     H_a: p < 100,000

H₀: μ = 100,000,     H_a: μ < 100,000     

H₀: p < 100,000,     H_a: p ≥ 100,000

H₀: μ ≥ 100,000,     H_a: μ < 100,000

H₀: p ≤ 100,000,     H_a: p > 100,000

H₀: μ < 100,000,     H_a: μ ≥ 100,000

H₀: μ ≤ 100,000,     H_a: μ > 100,000

H₀: p ≥ 100,000,     H_a: p < 100,000

D. Twenty-nine percent of high school seniors get drunk each month. (out of the following)

H₀: p < 0.29,     H_a: p > 0.29

H₀: μ = 29,     H_a: μ ≠ 29     

H₀: p ≠ 0.29,     H_a: p = 0.29

H₀: p = 0.29,     H_a: p > 0.29

H₀: μ = 29,     H_a: μ > 29

H₀: μ ≠ 29,     H_a: μ = 29

H₀: μ < 29,     H_a: μ > 29

H₀: p = 0.29,     H_a: p ≠ 0.29

E. Fewer than 5% of adults ride the bus to work in Los Angeles. (out of the following)

H₀: μ ≥ 5,     H_a: μ < 5

H₀: p ≥ 0.05,     H_a: p < 0.05     

H₀: p = 0.05,     H_a: p ≠ 0.05

H₀: μ < 5,     H_a: μ ≥ 5

H₀: p ≤ 0.05,     H_a: p > 0.05

H₀: μ ≤ 5,     H_a: μ > 5

H₀: p < 0.05,     H_a: p ≥ 0.05

H₀: μ = 5,     H_a: μ ≠ 5

F. The mean number of cars a person owns in her lifetime is not more than 10. (out of the following)

H₀: p = 10,     H_a: p ≠ 10

H₀: μ ≥ 10,     H_a: μ < 10     

H₀: p ≥ 10,     H_a: p < 10

H₀: μ ≤ 10,     H_a: μ > 10

H₀: p ≤ 10,     H_a: p > 10

H₀: μ = 10,     H_a: μ ≠ 10

H₀: μ < 10,     H_a: μ ≥ 10

H₀: p < 10,     H_a: p ≥ 10

G. About half of Americans prefer to live away from cities, given the choice.

H₀: p ≠ 0.50,     H_a: p = 0.50

H₀: μ = 1/2 , H_a: μ ≠ 1/2

H₀: p ≥ 0.50,     H_a: p < 0.50

H₀: p = 0.50,     H_a: p ≠ 0.50

H₀: μ ≥ 1/2 , H_a: μ = 1/2

H₀: μ ≠ 1/2 , _Ha: μ < 1/2

H₀: p ≤ 0.50,H_a: p > 0.50

H₀: μ ≤ 1/2 ,     H_a: μ > 1/2

H. Europeans have a mean paid vacation each year of six weeks. (out of the following)

H₀: p ≠ 6,     H_a: p = 6

H₀: μ ≥ 6,     H_a: μ < 6     

H₀: p = 6,     H_a: p ≠ 6

H₀: μ ≤ 6,     H_a: μ > 6

H₀: p ≤ 6,     H_a: p > 6

H₀: p ≥ 6,     H_a: p < 6

H₀: μ ≠ 6,     H_a: μ = 6

H₀: μ = 6,     H_a: μ ≠ 6

I. The chance of developing breast cancer is under 11% for women. (Out of the following)

H₀: μ < 11,     H_a: μ ≥ 11

H₀: μ ≤ 11,     H_a: μ > 11     

H₀: p < 0.11,     H_a: p ≥ 0.11

H₀: p ≤ 0.11,     H_a: p > 0.11

H₀: p = 0.11,     H_a: p ≠ 0.11

H₀: μ ≥ 11,     H_a: μ < 11

H₀: μ = 11,     H_a: μ ≠ 11

H₀: p ≥ 0.11,     H_a: p < 0.11

J. Private universities' mean tuition cost is more than $20,000 per year. (out of the following)

H₀: μ ≥ 20,000,     H_a: μ < 20,000

H₀: p > 20,000,     H_a: p ≤ 20,000    

H₀: p ≥ 20,000,     H_a: p < 20,000

H₀: p ≤ 20,000,     H_a: p > 20,000

H₀: μ ≤ 20,000,     H_a: μ > 20,000

H₀: μ = 20,000,     H_a: μ ≠ 20,000

H₀: μ > 20,000,     H_a: μ ≤ 20,000

H₀: p = 20,000,     H_a: p ≠ 20,000