A random sample of nn measurements was selected from a population with standard deviation σ=19.9σ=19.9 and unknown mean μμ. Calculate a 9595 % confidence interval for μμ for each of the following situations:

(a) n=60, x¯¯¯=95.6n=60, x¯=95.6
≤μ≤≤μ≤

(b) n=80, x¯¯¯=95.6n=80, x¯=95.6
≤μ≤≤μ≤

(c) n=100, x¯¯¯=95.6n=100, x¯=95.6
≤μ≤≤μ≤

(d) In general, we can say that for the same confidence level, increasing the sample size  the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)

Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 36 of the 43 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 95 of the 109 subjects developed rhinovirus infections. Use a 0.01 significance level to test the claim that echinacea has an effect on rhinovirus infections.

Complete parts (a) through (c) below.

a) Conduct an appropriate Hypothesis Test using  = 0.01 level of significance to determine if echinacea has an effect on rhinovirus infections. Include a conclusion that is in terms of the problem. 1. (2 pts.) State the Hypothesis: ?0: ?1:

2. (1 pt.) Determine the P-value.

3. (3 pts.) State your decision.

4. (4 pts.) State your conclusion in terms of the problem scenario. b)

Construct a 95% confidence interval to test the claim. Does the confidence interval agree with the conclusion of the hypothesis test? (You only need to include the confidence interval obtained from STATCrunch or Calculator) Explain your answer.

A pudding company has to ensure that they maintain strict oversight on the weight of a box of pudding they sell to their customers. Their advertisement states that the weight is between 290 and 310g per bottle of pudding. The company collected 15 bottles of pudding to measure their weight. The weight (gram) of each bottle are shown as follows. Use ?=0.0901

data: 306,290,289,309,289,307,301,307,302,298,295,295,291,289,296

Does the data suggest that the sample standard deviation in the weight per bottle compares to the hypothesised ?=43.9?

(a) Construct a 90.99% confidence interval estimate of the variance, σ2, of the weight per bottle

(b) What ?????????? needs to be satisfied for the inferences made in (a) to be valid? Use appropriate graph to check the normality assumption.

p-value =

(c) does the data above follow an approximately normal distribution?

(d) the data suggest that the standard deviation in weight (gram) per bottle is _____ 43.9?

[A] Significantly greater than

[B] Not significantly different from

[C] Significantly less than

**** LOOKING TO SOLVE THE SECOND PART TO THIS 2 PART QUESTION; PROBLEM 4 ONLY PLEASE ****

Automobiles arrive at the drive-through window at a post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.
a) What is the average time a car is in the system? 10 minutes
b) What is the average number of cars in the system? 4
c) What is the average time cars spend waiting to receive service? 8 minutes
d) What is the average number of cars in line behind the customer receiving service? 3.2
e) What is the probability that there are no cars at the window? 0.2
f) What percentage of the time is the postal clerk busy? 80%
g) What is the probability that there are exactly two cars in the system? 0.128

Problem-4:
For the post office in the previous problem, a second drive-through window is being considered. A single line would be formed and as a car reached the front of the line it would go to the next available clerk. The clerk at the new window works at the same rate as the current one.
• What is the average time a car is in the system?
• What is the average number of cars in the system?
• What is the average time cars spend waiting to receive service?
• What is the average number of cars in line behind the customer receiving service?
• What is the probability that there are no cars in the system?
• What percentage of the time are the clerks busy?
• What is the probability that there are exactly two cars in the system?

An article in Obesity Research “Impaired pressure natriuresis in obese youths,” (2003, Vol. 11, pp. 745–751) described a study in which all meals were provided for 14 lean boys for three days followed by one stress test (with a video-game task). The average systolic blood pressure (SBP) during the test was 118.3 mm HG with a standard deviation of 9.9 mm HG. Construct a 97.5% one-sided upper confidence interval for mean SBP. Assume population is approximately normally distributed. Round your answer to 3 decimal places.

The president of Doerman Distributors, Inc., believes that 25% of the firm's orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers.

(a)

Assume that the president is correct and

p = 0.25.

What is the sampling distribution of

p

for n = 100? (Round your answer for

σp

to four decimal places.)

σp

=

E(p)

=

Since np = and n(1 − p) = , approximating the sampling distribution with a normal distribution

appropriate in this case.

(b)

What is the probability that the sample proportion

p

will be between 0.15 and 0.35? (Round your answer to four decimal places.)

(c)

What is the probability that the sample proportion will be between 0.20 and 0.30? (Round your answer to four decimal places.)

Concept-Discussion 1 - Explain why the standard deviation would likely not be a reliable measure of variability for a distribution of data that includes at least one extreme outlier.

Concept-Discussion 2 - Suppose that you collect a random sample of 250 salaries for the salespersons employed by a large PC manufacturer. Furthermore, assume that you find that two of these salaries are considerably higher than the others in the sample. Before analyzing this data set, should you delete the unusual observations? Explain why or why not.

Concept-Discussion 3 - A researcher is interested in determining whether there is a relationship between the number of room air- conditioning units sold each week and the time of year. What type of descriptive chart would be most useful in performing this analysis? Explain your choice.

Concept-Discussion 4 - Suppose that the histogram of a given income distribution is positively skewed. What does this fact imply about the relationship between the mean and median of this distribution?

This is an exploratory problem intended to introduce the idea of curvilinear regression. Personally, I was a bit shocked to discover that multiple LINEAR regression is the main vehicle to calculate regressions for data with nonlinear relationships...sounds a bit counter-intuitive. However, if we think of the higher-power terms (quadratic, cubic, etc.) as distinct variables, the ideas work well together.

Here is a data set for students in a gifted program. The first score (X1=GPA) is the students’ math grade from last year, and the second score (Y=SAT) is their SAT-M score. As this is a non-representative group (when considering the population of all students taking math classes in high school), it is not unexpected to see range-restriction effects (generally all high performing, few lower performing representatives) or ceiling effects (maximum score on the SAT-M is 800). In data such as this, it is not uncommon to see non-linear trends.

Step 1: Copy the data into your preferred statistical software program. Change the variable names to GPA and SAT if need be. Before doing any analysis, look at a scatterplot of the data with GPA on the horizontal axis and SAT on the vertical axis. Be sure to note any trends.

The following includes information for Excel users. If you are not using Excel, please disregard.

Step 2: Run a regression (Data Analysis > Regression) with SAT as the X variable. Again, be sure to note what evidence supports the assumptions for a regression analysis. Report the regression equation and the requested statistics:

SAT=___+___×GPA
(Report regression coefficients accurate to 3 decimal places.)

R2adj=
(Report accurate to 3 decimal places.)

Step 3: Create a third variable called GPAsq (for squared GPA). In Excel, use a formula, something like =B1^2 and fill down the rest of the column.

Step 4: Run the quadratic regression by adding the independent variable GPAsq to the model. Report the regression equation and the requested statistics:

SAT=__+__ ×GPA + ___ ×GPA2
(Report regression coefficients accurate to 3 decimal places.)

R2adj=
(Report accurate to 3 decimal places.)

Step 5: Notice how the adjusted coefficient of multiple determination changed from the bivariate regression to the quadratic (multiple) regression. The next step is to determine if this more complicated model is statistically significantly better than the more parsimonious linear model.

For the multiple regression model, what was the F-ratio and the resulting P-value?
Fmodel=
(Report accurate to 2 decimal places.)
P=
(Report accurate to 3 decimal places.)

Using the statements provided in question one, determine if the statement is a null hypothesis or a research hypothesis

a. A. You are interested in finding out if the average household income of residents in your state is different from the national average household. According to the US Census, for 2011, the national average household income is $50,054.

STATEMENT: The average household income of residents in your state is different than the national average household income.

b. You believe that students in small liberal arts colleges attend more parties per month than students nationwide. It is known that nationally undergraduate students attend as average of 3.2 parties per month. The average number of parties per month will be calculated from a random sample of students from small liberal arts colleges.

STATEMENT: The number of parties that students at a small liberal arts college attend is greater than the national average among undergraduate students.

c.  A sociologist believes that the average income of elderly women is lower that the average income of elderly men

STATEMENT: The average income of elderly women is less than the average income of elderly men.

d. Is there a difference in the amount of study time on-campus and off-campus students devote to their schoolwork during an average week? You prepare a survey to determine the average number of study hours for each group of students.

STATEMENT: The amount of hours students spend studying on campus is the same as the amount of hours spent studying off campus.

e.  Reading scores for a group of third graders enrolled in an accelerated reading program are predicted to be higher than the scores for non-enrolled third graders.

STATEMENT: The reading scores of third graders in an accelerated reading program are higher than non-enrolled third graders.

f. Stress (measured on an ordinal scale) is predicted to be lower for adults who own dogs (or other pets) than for non-pet owners.

STATEMENT: Stress is lower for dog owners than it is for non-pet owners.

Giving a test to a group of students, the grades and gender are summarized below

A B C Total

Male 18 16 6 40

Female 13 19 15 47

Total 31 35 21 87

Let p represent the population proportion of all female students who received a grade of B on this test. Use a 99% confidence interval to estimate p to four decimal places if possible. < p <

The amount of time a bank teller spends with each customer has a population mean of 3.086 minutes. You select a random sample of 16 customers. The sample standard deviation is 0.40 minutes. There is a 95% chance that the sample mean is below ______ minutes

You have just read an interesting article titled, “High School Students’ Perceptions of Their Peers.” In the article, the researchers asked 2500 Canadian high school students various questions relating to their perceptions of other students. The average perception of student cool, on a coolness scale from 1 (not cool) to 10 (extremely cool), was 5 with a standard deviation of 1 and normally distributed. You have a theory that high school students who regularly skateboard to school will be perceived as cooler than students in the general population. You survey 10 students regarding their perceptions of skateboarder coolness using the same scale as the researchers in the article. Your results are tabled below:

From the information given above, carry out the 5-steps of hypothesis testing outlined in chapter

6 of your text and/or study notes for unit 4. Hint: You have a sample size of 10! So root 10 might

have to come into play! Note: Be sure to end with a conclusion regarding your retention or

rejection of the null hypothesis

A sample consisting of 430 men and 775 women was asked various questions pertaining to international affairs. With a 90% level of confidence, find the margin of error associated with the following samples. (Round your answers to one decimal place.) (a) the male sample ± % (b) the female sample ± % (c) the combined sample ± %

Use the sample data and confidence level given below to complete parts​ (a) through​ (d).

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll,

n=988 and x=505 who said​ "yes." Use a 99% confidence level.

a) Find the best point estimate of the population proportion p.

​b) Identify the value of the margin of error E.

​c) Construct the confidence interval.

< p <

​d) Write a statement that correctly interprets the confidence interval.