Problem 2.3 Suppose that we take the universal set U to be the integers. Let S be the even integers, letT be the integers that can be obtained by tripling any one integer and adding one to it, and let V be the set of numbers that are whole multiples of both two and three.

(i) Write S, T, and V using symbolic notation.

(ii) ComputeS∩T, S∩V andT∩V and give symbolic representations that do not use the symbols S, T, or V on the right-hand side of the equals sign.

A company wants to ship products from Jefferson City and Omaha to Des Moines, Kansas City or St. Louis.

In the table below you see shipping costs and supply and demand amounts.

How do you set this up in Excel through the Solver? Please show the steps. Thanks!

To evaluate the effectiveness of a new type of plant food developed for tomatoes, an experiment was conducted in which a random sample of 56 seedlings was obtained from a large greenhouse having thousands of seedlings. Each of the 56 plants received 80.5 grams of this new type of plant food each week for 9 weeks. The number of tomatoes produced by each plant was recorded yielding the following results: ?bar =31.08 . ?=4.325

A researcher has started with a new sample and a given degree of confidence that the average number of tomatoes the seedlings produced on the new plant food is between "35.64258 and 37.63742". Suppose the sample size and standard deviation are the same as given above. What alpha did the researcher use in the construction of this statement?

f(x) = 3e −3x x > 0

0 otherwise.

Find the expected value and variance of the random variable.

The birthweight of newborn babies is Normally distributed with a mean of 3.39 kg and a standard deviation of

0.55 kg.

(a) Find the probability that a baby chosen at random will have a birthweight of over 3.5 kg.

(b) Find the probability that an SRS of 16 babies will have an average birthweight of over 3.5 kg.

(c) Find the probability that an SRS of 100 babies will have an average birthweight of over 3.5 kg.

(d) What range of average birthweights would the largest 15% of samples of size 100 babies have?

You may believe that each day, married and unmarried women spend the same amount of time per week using Facebook. We would like to test this hypothesis. A random sample of 45 married women who use Facebook spent an average of 3.0 hours per week on this social media website. A random sample of 39 unmarried women who regularly use Facebook spent an average of 3.4 hours per week. Assume that the weekly Facebook time for married women has a population standard deviation of 1.2 hours, and the population standard deviation for unmarried Facebook users is 1.1 hours per week. Using the 0.05 significance level, do married and unmarried women differ in the amount of time per week spent on Facebook? State the decision rule for 0.05 significance level: H0: μ married = μ unmarried H1: μ married ≠ μ unmarried. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) Compute the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) What is the p-value? (Round your answer to 4 decimal places.) State your decision about the null hypothesis. Fail to reject H0 Reject H0

A sample of 16 joint specimens of a particular type gave a sample mean proportional limit stress of 8.55 MPa and a sample standard deviation of 0.79 MPa.

a)Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)

b)Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two decimal places.)

The mean volume of customer traffic in a new store is 927 people per week with a standard deviation of 86. Answer the following questions based on these data. Write out what P() would be for each.

a. What is the probability that more than 1,000 customers visit the store in a given week?

b. What is the probability that less than 800 customers visit the store in a given week?

c. What is the probability that between 900 and 1050 customers visit the store in a given week?

1. Z is a standard normal variable. Find the value of Z in the area to the left of Z is 0.9279. The area to the right of Z is 0.1539.

2. Given that x is a Normal random variable with a mean of 10 and standard deviation of 4, find the following probability:

     P(8.8<x<12.5)

A report classified fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table.

(a) Use the given data to test the null hypothesis H₀: p₁ = 1/12, p₂= 1/12, .., p₁₂= 1/12, where p1 is the proportion of fatal bicycle accidents that occur in January, p2 is the proportion for February, and so on. Use a significance level of 0.01.

Calculate the test statistic. (Round your answer to two decimal places.)

χ² =

What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.)

P-value =

What can you conclude?
Reject H₀. There is not enough evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.
Do not reject H₀. There is not enough evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.
Do not reject H₀. There is convincing evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.
Reject H₀. There is convincing evidence to conclude that fatal bicycle accidents are not equally likely to occur in each of the months.

(b) The null hypothesis in part (a) specifies that fatal accidents were equally likely to occur in any of the 12 months. But not all months have the same number of days. What null and alternative hypotheses would you test to determine if some months are riskier than others if you wanted to take differing month lengths into account? (Assume this data was collected during a leap year, with 366 days.) (Enter your probabilities as fractions.)

Identify the null hypothesis by specifying the proportions of accidents we expect to occur in each month if the length of the month is taken into account. (Enter your probabilities as fractions.)

p₁= p₂= p₃=   p₄= p₅= p₆=   p₇= p₈= p₉= p₁₀= p₁₁= p₁₂=

Identify the correct alternative hypothesis.

H₀ is true. None of the proportions is not correctly specified under H₀.
H₀ is not true. At least one of the proportions is not correctly specified under H₀.
H₀ is true. At least one of the proportions is not correctly specified under H₀.
H₀ is not true. None of the proportions is correctly specified under H₀.

(c) Test the hypotheses proposed in part (b) using a 0.05 significance level.

Calculate the test statistic. (Round your answer to two decimal places.)

χ² =

What is the P-value for the test? (Use a statistical computer package to calculate the P-value. Round your answer to four decimal places.)

P-value =

What can you conclude?
Reject H₀. There is not enough evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.
Do not reject H₀. There is convincing evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.
Do not reject H₀. There is not enough evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.
Reject H₀. There is convincing evidence to conclude that fatal bicycle accidents do not occur in the twelve months in proportion to the lengths of the months.

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 9 students, taught in traditional lab sessions, had a mean test score of 71.5 with a standard deviation of 4.1. A random sample of 6 students, taught using interactive simulation software, had a mean test score of 77.9 with a standard deviation of 4.7. Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ1 be the mean test score for the students taught in traditional lab sessions and μ2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.05

for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 3 of 4 :

Determine the decision rule for rejecting the null hypothesis H0

. Round your answer to three decimal places.

Reject H0 if t/or |t|, (<, or >) _________

Consider the following hypotheses:

H₀: μ = 3,900
H_A: μ ≠ 3,900

The population is normally distributed with a population standard deviation of 510. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can "reject/do not reject" the null hypothesis at the 10% significance level. (You may find it useful to reference the appropriate table: z table or t table) (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round "test statistic" values to 2 decimal places and "p-value" to 4 decimal places.)

What three independent variables could I use for geographical statistical model? Please give examples of how to use.

Based on the data given, find the Null Hypothesis and Research Hypothesis using 0.05 for two tails.

Does fast food actually cause Obesity?

Eating fast food does not make one obese.

Is the sugar served in fast food restaurant responsible for heart disease?

Heart disease is not cause by sugar.

Find the correlation amount the two sets of data