Samples of computers are taken from two county library locations and the number of internet tracking spyware programs is counted. The first location hosted 21 computers with a mean of 4.1 tracking programs and a standard deviation of 0.8. The second location hosted 19 computers with a mean of 6.2 tracking programs and a standard deviation of 1.2.

a) Please calculate the appropriate standard error statistic for the scenario provided.

b)Please calculate a confidence interval around your point estimates as appropriate for the scenario. Use a confidence limit of 99% (.01)

c) Please calculate a confidence interval around your point estimates as appropriate for the scenario. Use a confidence limit of 95%.

d) How do your confidence intervals compare? Is this what you expected to see? Why?

Directions: Show ALL work! Please round any answer to the nearest hundredth, unless you can get an exact amount. If an answer asks to explain, please make sure to give a valid and complete explanation. For your hypothesis tests, make sure you give a complete interpretation.

2. In a survey of 500 randomly selected U.S. teens, it was found that 37% of them have been in the car while a person under the influence is driving.

a) Construct a 90% confidence interval for the population proportion of U.S. teens who have been in the car while a person under the influence is driving.

b) Using the information from part a, determine the minimum sample size required to be 95% confident that the estimate is accurate within 3% of the population proportion.

Do male and female students study the same amount per week? In 2007, 58 sophomore business students were surveyed at a large university that has more than 1,000 sophomore business students each year. The table beloe has the gender and hours spent studying in a typical week for the sampled students.

a. At the 0.05 significance level, is there a difference in the variance of study time for male students and female students? (1 point)

b. Using the results of part (a), which t-test is appropriate for comparing the mean study time for male and female students? (1 point)

c. At the 0.05 significance level, conduct the test selected in part (b) (1 point)

d. Write a short summary of your findings (1 point)

Part 2: For each hypothesis question (6 - 8): (a) state the claim mathematically, (b) identify the null and
alternate hypotheses, (c) determine the type of test to be used, (d) calculate the test statistic, (e) use
either the p-value or critical region method to test the claim, (f) determine whether to reject or fail to
reject the Null Hypothesis, (g) state your conclusion.

6. Fandango claim’s that the average cost of a movie ticket is at least $8.75 for an adult, with a known variance of $0.25. To test this claim, a random sample of 75 tickets had a mean of $8.06. There is no reason to think the variance is any different in the sample. Based upon this information, can we reject Fandango’s claim at the 5% level of significance?

The results of inspection of samples of a product taken over the past 5 days are given below. Sample size for each day has been 100:

Find the center line (CL).

We are interested in studying the linear relationship between someone's age and how much they spend on travel. The following data is provided:

Find MSE (s-squared/ s^2).

A student at a university has been doing a project to investigate entertainment habits of students. They have surveyed 100 random students who were each asked three questions:

1. Have you watched a movie in the last week?
2. Have you listened to music in the last week?
3. Have you read a book in the last week?

However, the student keeps a very messy room and has lost some of the results. They have been able to find the following results:

Of all the students surveyed, 46 had watched a movie, 36 had listened to music and 41 had read a book in the last week. Also:

• 4 students answered yes to all three questions
• 10 students answered yes to questions 1 and 2 only
• 12 students answered yes to questions 1 and 3 only
• 20 students answered yes only to question 1
• 18 students answered no to all three questions

Find the missing information and answer the following questions regarding the group surveyed. Give your answers as whole numbers.

Calculate the number of students that:

a)answered yes to question 3 only =

b)answered yes to exactly two questions =

c)had watched a movie or listened to music but had not read a book =

which statistical analysis to use for a survey on a group of 6 people of 3 questions with four choices each strongly positive, positive, neutral and not positive and show an example

: An observational study is conducted to investigate the association between age and total serum cholesterol. The correlation is estimated at r = 0.35. The study involves n=125 participants and the mean (std dev) age is 44.3 (10.0) years with an age range of 35 to 55 years, and mean (std dev) total cholesterol is 202.8 (38.4).

a. Estimate the equation of the line that best describes the association between age (as the independent variable) and total serum cholesterol.

b. Estimate the total serum cholesterol for a 50-year old person.

c. Estimate the total serum cholesterol for a 70-year old person.

d. For part c, why or why not might this estimate be appropriate?

1. Weakly earnings on a certain import venture are approximately normally distributed with a known mean of $487 and unknown standard deviation. If the proportion of earnings over $517 is 27%, find the standard deviation. Answer only up to two digits after decimal.

2.X is a normal random variable with mean μ and standard deviation σ. Then P( μ− 1.4 σ ≤ X ≤ μ+ 2.2 σ) =? Answer to 4 decimal places.

3.Suppose X is a Binomial random variable with n = 32 and p = 0.41.

Use binomial distribution to find the exact value of   P(X < 11). [Answer to 4 decimal places]

What are the appropriate values of mean and standard deviation of the normal distribution used to approximate the binomial probability?
μ = 13.12, and σ = 0.087.
μ = 13.12, and σ = 2.782.
μ = 13.12, and σ = 7.741.
μ = 32, and σ = 0.41.

Using normal approximation, compute the approximate value of   P(X < 11). [Answer to 4 decimal places]

Is the n sufficiently large for normal approximation?
Yes, because n is at least 30.
No, because μ±3σ, is contained in the interval (0, 32).
Yes, because μ±3σ, is inside the interval (0, 32).
No, because np < 15

4. Usually about 65% of the patrons of a restaurant order burgers. A restaurateur anticipates serving about 155 people on Friday. Let X be the numbers of burgers ordered on Friday. Then X is binomially distributed with parameters n = 155 and p = 0.65.

What is the expected number of burgers (μ_X) ordered on Friday? [Answer up to 2 digits after decimal]

Find the standard deviation of X (σ_X)? [Answer up to 3 digits after decimal]

If the restaurant ordered meats to prepare about 109 burgers for Friday evening. Use normal approximation of binomial distribution to find the probability that on Friday evening some orders for burgers from the patron cannot be met. [Answer up to 4 digits after decimal]

How many burgers the restaurant should prepare beforehand so that the chance that an order of burger cannot be fulfilled is at most 0.05? i.e. Find a such that P(X > a) = 0.05 using normal approximation of binomial distribution.

Problem 8: The Framingham Heart Study was a longitudinal cohort study of 5000+ men and women. One outcome of interest was fasting glucose levels. Glucose levels were categorized into three different categories:

Glucose Levels

     -Diabetes (glucose >126),

    -Impaired Fasting Glucose (glucose 100-125),

    -Normal Glucose

Several possible risk factors were also recorded:

Risk Factors

     -Sex

     -Age

     -BMI (normal weight, overweight, obese)

     -Genetics

To determine if each possible risk factor is related to glucose levels,researchers need to use an appropriate hypothesis test.

Test Choices

1. ANOVA

2. Chi-Square GOF

3. Chi-Square test for independence

4. Test for equality of means

5. Test for equality of proportions

6. Other

a. What test would be used to assess whether the different sexes(male and female) have the same proportions of the different glucose levels?

b. What test would be used to assess whether the different glucose levels have the same mean age?

c. What test would be used to assess whether the different categories of BMI have the same proportions of the different glucose levels?

which statistical analysis to use for a survey of 5 questions with four choices each strongly positive, positive, neutral and negative

How does confidence intervals confirm hypothesis testing results. Provide an example

Use the applet "Sample Size and Interval Width when Estimating Proportions" to answer the following questions.

This applet illustrates how sample size is related to the width of a 95% confidence interval estimate for a population proportion.

(a)

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.023?

(b)

As the sample size decreases for any given confidence level, what happens to the confidence interval?

The width of the confidence interval becomes the same as the standard error.The confidence interval becomes more narrow because the sampling distribution becomes larger.    The confidence interval becomes wider because the standard error becomes larger.The confidence interval becomes wider than the population proportion.The confidence interval becomes more narrow than the population proportion.

You work for a lobby group that is trying to convince the government to pass a new law. Before embarking on this, your lobby group would like to know as much as possible about the level of community support for the new law.

Your colleague, based on his research into community opinion on related matters, proposes that 32% of the community support the law. You decide to survey 100 people, and find that 27% of this survey support the law.

a)Based on the assumption that the population proportion is 32%, calculate the z-score of the sample proportion in your survey. Give your answer as a decimal to 2 decimal places.

z =

b)Determine the proportion of the standard normal distribution that lies to the left of this z-score. That is, determine the area to the left of this z-score in the standard normal distribution. You may find this standard normal table useful. Give your answer as a percentage to 2 decimal places.

Area =  %

c)Denote by x% the percentage proportion you calculated in part b). Consider the following five potential conclusions:

A: There is a chance of x% that your friend is correct, that the true population proportion is 32%.

B: If your colleague is correct and the true population proportion is 32%, then x% of all samples will produce a sample proportion of 27% or lower.

C: If your colleague is correct and the true population proportion is 32%, then x% of all samples will produce a sample proportion of 27% or higher.

D: There is a chance of x% that the true population proportion is 32% or lower.

E: There is a chance of x% that the true population proportion is 32% or higher.

Select the statement that can be inferred from your findings:

A
B
C
D
E