The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following show the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older. Hours of Sleep Age Fewer than 6 6 to 6.9 7 to 7.9 8 or more Total 49 or younger 37 58 71 74 240 50 or older 34 60 79 87 260

a.Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use = .05.

Compute the value of the 2 test statistic (to 2 decimals).

b.Using the total sample of 500, estimate the percentage of people who sleep less than 6, 6 to 6.9, 7 to 7.9, and 8 or more hours on weeknights (to 1 decimal).

Less than 6 hours %

6 to 6.9 hours %

7 to 7.9 hours %

8 or more hours %

A 0.01 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is different from 0.5. Assume that sample data consists of 66 girls in 144 births, so the sample statistic of 11/24 results in a z score that is 1 standard deviation below 0.

a. Identify the null hypothesis and the alternative hypothesis. Choose the correct answer below.

A.H0​:p=0.5

H1​:p>0.5

B. H0​: p≠0.5

   H1​: p=0.5

C.H0​: p=0.5

H1​: p<0.5

D.H0​: p=0.5

H1​: p≠0.5

b. What is the value of α​?

α=________

​(Type an integer or a​ decimal.)

c. What is the sampling distribution of the sample​ statistic?

Normal distribution

χ2

Student​ (t) distribution

d. Is the test​ two-tailed, left-tailed, or​ right-tailed?

___________

e. What is the value of the test​ statistic?

The test statistic is ____________

f. What is the​ P-value?

The​ P-value is _____________

g. What are the critical​ value(s)?

The critical​ value(s) is/are ________

h. What is the area of the critical​ region?

The area is ________

For a newsvendor product the probability distribution of demand X (in units) is as follows:

xi 0 1 2 3 4 5 6
pi 0.05 0.1 0.2 0.3 0.2 0.1 0.05

The newsvendor orders Q = 4 units.

a) Derive the probability distributions and the cumulative distribution functions of lost sales as well as leftover inventory.

b) Knowing that the expected total cost function is convex in the order quantity Q, demonstrate that Q = 4 gives the minimal expected total cost.

The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. A paper described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on this data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.7 mm and a standard deviation of 4.2 mm.

(a)

Approximately what proportion of healthy children have left atrial diameters less than 24 mm? (Round your answer to four decimal places.)

(b)

Approximately what proportion of healthy children have left atrial diameters greater than 32 mm? (Round your answer to four decimal places.)

(c)

Approximately what proportion of healthy children have left atrial diameters between 25 and 30 mm? (Round your answer to four decimal places.)

(d)

For healthy children, what is the value for which only about 20% have a larger left atrial diameter? (Round your answer to two decimal places.)

You may need to use the appropriate table in Appendix A to answer this question.

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.

a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean?

b. What is the probability that these 64 students will spend an average of more than $11 per person?

c. What is the probability that these 64 students will spend an average between $10 and $11 per person?

suppose a woman wants to estimate her exact day of ovulation for contraceptive purposes. A theory exists that at the time of ovulation the body temperature rises 0.5 to 1.0 degrees F thus, changes in body temperature can be used to goes the day of ovulation.

suppose that for this purpose a woman measures her body temperature on awakening on the first 10 days after menstruation and obtains the following data: 95.8, 96.5, 97.4, 97.4, 97.3, 96.0, 97.1, 97.3, 96.2, 97.3.

A. what is the best point estimate of her underlying basal body temperature (population mean)

b. how precise is this estimate (calculate the standard error of the estimate)?

c. compute a 95% confidence interval for the underlying mean basal body temperature using the data. assume that her underlying mean basal body temperature has a normal distribution

Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a mean of 8.7 minutes with a standard deviation of 8.7 minutes. Using only the values of these two parameters and your knowledge of the properties of the Normal distribution, give an argument why it is unreasonable to assume that the time between arrivals of buses is normally distributed (or even approximately so). (Hint: Consider the range of data of a Normal distribution.)

A baseball coach reviews the number of runs hit per game for the past several seasons. Since the team plays so many games, he selects a random sample of 10 games and records the number of runs scored in each game. The average number of runs scored is 7 with a standard deviation of 3.1 runs.

Compute the margin of error given a confidence level of 99%. (Use a table or technology. Round your answer to three decimal places.)

Working backwards, Part I. A 90% confidence interval for a population mean is (83, 89). The population distribution is approximately normal and the population standard deviation is unknown. This confidence interval is based on a simple random sample of 25 observations. Calculate the sample mean, the margin of error, and the sample standard deviation. Use the t distribution in any calculations. Round non-integer results to 2 decimal places.

Sample mean =

Margin of error =

Sample standard deviation =

Below is a distribution of race in the United States from 2014.

White= 60.5%

Black= 12.5%

Hispanic= 18.3%

Asian= 5.7%

Other= 3%

If we were to randomly choose 150 people for a survey, what is the probability that less than 70 of them would be white (round to 3 decimal places)?

Would this be unusual? If so, give some reasons why a particular sample might have less than 70 whites.

What is the probability that we would randomly choose a sample of 150 people and more than 22 of them were black (to 3 decimal places)?

What is the probability you would randomly select two Americans and they would both be white?

How many Asian people should we expect to have in a randomly selected group of 150 people?

Delta airlines quotes a flight time of 2 hours, 5 minutes for its flight from Cincinnati to Tampa. Assume that the probability of a flight time within any one-minute interval is the same as the flight time within any other one-minute interval contained within the larger interval, 120 and 140 minutes.

*State the objective: What is the probability that the flight will be no more than 5 minutes late?

•Q1: What pdf best describes (models) the situation or assigns probabilities to outcomes of r.v.?

•Q2: Name and given values for parameters in the pdf.

•Q3: Define r. v.?

•Q4: Is r.v. discrete or continuous? (Make sure consistent with Q1)

•Q5: Write down the objective, question, or problem statement and then translate the English version into a statistics problem (using statistical and math language/formulas)

•Q6: Solve the objective.

Read the following statements and decide if they are true sometimes, always or never. Be sure to give a reason for each statement or use an example and the reason why it shows the statement is false. You can download this document in the module one section Fractions and attach it if you prefer.

1. All fractions are less than one
2. Improper fractions are greater than or equal to one
3. Proper fractions are less than one
4. Fractions are always part of a whole
5. All Fractions can be written as terminating decimals.
6. When you create an equivalent fraction, you are multiplying by one.
7. Numerators and denominators are always the same.

These questions come from MBA 5008

1. What is the difference between a point estimate and a confidence interval?

2. Is a point estimate alone is adequate?

3. Evaluating the effect of variability measurement (confidence interval) on the resulting estimates.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

A coin mint has a specification that a particular coin has a mean weight of 2.5 g. A sample of 36 coins was collected. Those coins have a mean weight of 2.49502g and a standard deviation of 0.01562

Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5g

Do the coins appear to conform to the specifications of the coin​ mint?

test statistic z=

p=