In a few more weeks, you will be adding a new member to your family – a 10-week old golden retriever puppy! In previous litters, the average weight of 42 puppies at 10 weeks was 14.8 lbs with a standard deviation of 1.1 lbs.

Find the 90% confidence interval for the average 10-week weight for golden retriever puppies. Show/explain your work, and identify the following:

a. The estimated population mean and degrees of freedom

b. The assumptions you are making for this calculation

c. The critical value for the distribution

d. The margin of error

e. The 90% CI, stated as a complete sentence

They main goal is to find either a Z score or T score for the data below

What is the population mean and the sample mean for the elevations (in feet) of the trails below:

Mount Chocorua via Liberty Trail: 2,502 feet of elevation gain

Welch-Dickey Loop: 1,807 feet of elevation gain

Lonesome Lake Trail: 1,040 feet of elevation gain

Mount Willard: 985 feet of elevation gain

Red Hill Fire Tower: 1,350 feet of elevation gain

Pack Monadnock: 840 feet of elevation gain

Mount Cardigan’s Holt Trail: 1,800 feet of elevation gain

Mount Washington via Tuckerman Ravine: 4,238 feet of elevation gain

Presidential Traverse: 4,989 feet of elevation gain

Mount Moosilauke: 2,342 feet of elevation gain

The Carters: 3,305 feet of elevation gain

Mount Carrigain via Signal Ridge: 3,257 feet of elevation gain

Mount Flume + Mount Liberty Loop: 3,099 feet of elevation gain

Mount Isolation via glen boulder trail: 4,931 feet of elevation gain

Mount Monroe Trail: 2,572 feet of elevation gain

Maine

Hunt and Helon Taylor trail: 8,021 feet of elevation gain

Katahdin Loop Trail: 3,894 feet of elevation gain

Abol Trail: 3,950 feet of elevation gain

Hunt Trail: 4,169 feet of elevation gain

Mount Katahdin and Hamlin peak Trail: 4,438 feet of elevation gain

Baxter Peak Via Saddle Trail: 3,832 feet of elevation gain

Knife Edge Trail: 3,987 feet of elevation gain

Dudley Trail: 5,360 feet of elevation gain

Chimney pond Trail: 1,463 feet of elevation

Katahdin North Loop Trail: 4,061 feet of elevation gain

Doubletop Mountain Trail: 4,704 feet of elevation gain

Big Spencer Mountain Trail: 1,820 feet of elevation gain

North traveler Mountain Trail: 3,694 feet of elevation gain

Big Moose Mountain Trail: 1,843 feet of elevation gain

Cranberry Peak Trail: 2,070 feet of elevation gain

I was to choose 30 hiking trails (15 from New Hampshire and 15 from Maine) and record their elevations. My hypothesis for this is I believe that the mean is greater then or equal to 2,500ft. I'm having trouble figuring out my population mean and my sample mean. Also I need to find out my z score or t score and show a graph showing whether its left or right tailed or both.

What role do variability and statistical methods play in controlling quality?

(16.19) A class survey in a large class for first-year college students asked, "About how many hours do you study in a typical week?". The mean response of the 427 students was x¯¯¯ = 17 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation 8 hours in the population of all first-year students at this university. What is the 99% confidence interval (±0.001) for the population mean? Confidence interval is from to hours.

1. A new restaurant keeps track of the number of nightly customers at monthly intervals over the course of a year. The restaurant has done very little advertising; most of its publicity is by word of mouth but its number of customers is increasing. The restaurant does not have a seasonal difference in number of customers (for example, no summer crowds).

1. Using the data below, fit each an exponential regression model to the data using Excel.

Month	Nightly customers
0	35
1	41
2	46
3	54
4	66
5	84
6	103
7	117
8	141
9	180
10	222
11	275

1. Write down your regression equation.

2. Enter the regression equation into your calculator and use the table feature to estimate when the restaurant will have 400 people.

3. What does the model predict about the number of customers in 18 months?

4. What does the model predict as time goes on? For example how many customers will be at the restaurant in 300 months (25 years), is this reasonable?

5. What is the growth rate of your regression equation? Find and interpret it.

Answer questions 33, 34, and 35 on separate sheets of paper and turn in with your scantron.

The ages of the Vice Presidents of the United States at the time of their death are listed below. Construct a frequency distribution to summarize the data. Use 6 classes. List the relative and cumulative frequencies. List the class boundaries and class midpoints. Use Excel to construct a histogram to display the data.

90	83	80	73	70	51	68	79	70	71	72
74	67	54	81	66	62	63	68	57	66	96
78	55	60	66	57	71	60	85	76	98	77
88	78	81	64	66	77	70

Refer to the data set in question 33 above. Construct a stem and leaf plot to depict the ages of the vice-presidents at the time of their deaths.

Use EXCEL to construct a Pareto chart for the number of tons (in millions) of trash recycled per year by Americans based on an Environmental Protection Agency study.

Type	Amount
Paper	320
Iron/steel	282
Aluminum	268
Yard waste	242
Glass	196
Plastics	42

A regression analysis is conducted with 13 observations.

a. What is the df value for inference about the slope betaβ​?

b. Which two t test statistic values would give a​ P-value of

0.05 for testing H0​:β =0 against Ha​: β ≠​0?

c. Which​ t-score would you multiply the standard error by in order to find the margin of error for a

95%confidence interval for betaβ​?

In a test of the hypothesis that the population mean is smaller than 50, a random sample of 10 observations is selected from the population and has a mean of 47.0 and a standard deviation of 4.1. Assume this population is normal.

a) Set up the two hypotheses for this test. Make sure you write them properly.

b) Check the assumptions that need to hold to perform this hypothesis test.

c) Calculate the t-statistic associated with the sample.

d) Graphically interpret the p-value for this test, that is, i) draw a (nice) graph with a t-distribution (remember of the number of degrees of freedom) ii) locate on the graph the t-statistic you found in part (c) iii) mark the P-value on the graph

e) Calculate the P-value for this test.

f) Statistically interpret the P-value for this test.

g) Let the level of significance α = 2.5%. Using P-value, make a conclusion for your test (write a complete sentence for full credit).

h) Let the level of significance α = 2.5%. Find the related critical value tα.

i) What is the rejection region (RR) implied by α = 2.5% ?

j) Draw the RR on your graph on page 1, part (d).

k) Using the RR, make a conclusion for your test (write a complete sentence for full credit).

Suppose x has a normal distribution with mean μ = 28 and standard deviation σ = 4.

a) Describe the distribution of x values for sample size n = 4. (Round σ_x to two decimal places.)

μx	=
σx	=

b) Describe the distribution of x values for sample size n = 16. (Round σ_x to two decimal places.)

μx	=
σx	=

c) Describe the distribution of x values for sample size n = 100. (Round σ_x to two decimal places.)

μx	=
σx	=

d) How do the x distributions compare for the various samples sizes?

I. The means are the same, but the standard deviations are decreasing with increasing sample size.

II. The standard deviations are the same, but the means are decreasing with increasing sample size.    

III. The means and standard deviations are the same regardless of sample size.

VI. The means are the same, but the standard deviations are increasing with increasing sample size.

V. The standard deviations are the same, but the means are increasing with increasing sample size.

1. Police response time to an emergency call is the difference between the time the call is first received and the time a patrol car arrives at the scene. Over along period of time, it has been determined that the police response time is normally distributed with a mean of 8.4 minutes and a standard deviation of 7 minutes. For a randomly received emergency call, what is the probability that the response time will be:
   1. Between 5 and 10 minutes
   2. Less than 5 minutes
   3. More than 10 minutes

QUESTION 1

1. Which of the following scenarios are most suitable for the chi-square test for difference in proportions?
   Hint: There are 3 correct answers.

   	a.	You want to know whether there is any difference between the average number of females and the average number of males who prefer working for a boss of the opposite gender as compared to a boss of the same gender.
   	b.	You are curious to find out if there is any difference in the average incomes among the U.S., Canada and the U.K.
   	c.	You wonder whether there is any difference in the proportions of smokers between female high school students and male high school students.
   	d.	You are interested in finding out whether the proportions of students who agree that NAU should increase its tuition further are the same across freshmen, sophomores, juniors and seniors.
   	e.	You are interest in finding out whether the percentages of PCs that break down within the first month are the same across five different manufacturers.
   	f.	You want to know whether the percentage of republicans who favor a tax cut is higher than the percentage among democrats.

QUESTION 2

1. Which of the following scenarios are most suitable for the chi-square test for independence?
   Hint: There are 2 correct answers.

   	a.	You want to know if there is any connection between a person’s hair color and eye color.
   	b.	You want to know whether there is any difference between the average number of females and the average number of males who prefer working for a boss of the opposite gender as compared to a boss of the same gender.
   	c.	You are curious to find out if the variations of smokers are the same across freshmen, sophomores, juniors and seniors at NAU.
   	d.	You wonder whether political party affiliation is related to gender.
   	e.	You are curious to find out if there is any difference in the average incomes among the U.S., Canada and the U.K.
   	f.	You want to know whether median income of republicans are higher than the median income of democrats.

QUESTION 3

1. Which of the following scenarios are most suitable for the Z test for difference in two proportions?
   Hint: There are 2 correct answers.

   	a.	You are interested in finding out whether the proportions of students who agree that NAU should increase its tuition further are the same across freshmen, sophomores, juniors and seniors.
   	b.	You are interest in finding out whether the percentages of PCs that break down within the first month are the same across five different manufacturers.
   	c.	You wonder whether political party affiliation is related to gender.
   	d.	You want to know if there is any connection between a person’s hair color and eye color.
   	e.	You wonder whether there is any difference in the proportions of smokers between female high school students and male high school students.
   	f.	You want to know whether the percentage of republicans who favor a tax cut is higher than the percentage among democrats.
   	g.	You are curious to find out if there is any difference in the average incomes among the U.S., Canada and the U.K.
   	h.	You want to know whether there is any difference between the average number of females and the average number of males who prefer working for a boss of the opposite gender as compared to a boss of the same gender.

QUESTION 4

1. When should the Marascuilo procedure be used?

   	a.	To find out if there is any difference in any pair of population proportions when one fails to reject the chi-square test for two proportions.
   	b.	To find out if there is any difference in any pair of population proportions once the chi-square test for more than two proportions is rejected.
   	c.	To find out if there is any difference in any pair of population porportions when one fails to reject the chi-square test for more than two proportions.
   	d.	To find out if there is any difference in any pair of population proportions once the chi-square test for two proportions is rejected.

QUESTION 5

1. The computation and operation procedure of the chi-square test for independence is exactly the same as those of which of the following?
   One correct answer.

   	a.	one-way ANOVA F test
   	b.	Z test for difference in two proportions
   	c.	Tukey-Kramer procedure
   	d.	Chi-square test for difference in more than two proportions
   	e.	Marascuilo procedure
   	f.	Z test for difference in two means

A chemist measures the haptoglobin concentration (in grams per litre) in the blood serum from a random sample of 11 healthy adults. The concentrations are assumed to be normally distributed and are given below.

1.4,1,1.8,1.8,0.4,1.5,2.2,0.8,0.9,3.3,2.2

At a 1% level of significance, perform a statistical test to see if there is evidence that the mean haptoglobin concentration in adults is less than 1.8 grams per litre, by answering the following parts.

1.1 (.8 marks)

Give the Null and Alternative Hypotheses, using mu to denote the population mean. H0 : 1.1.2 (.4 marks) HA : 1.2 (.2 marks) What's the significance level α? α =   1.3 (1 mark) Find the value of the test statistic correct to 2 decimal places. t ≈   1.4 (1 mark) What is the p-value? Give your answer to 3 decimal place accuracy. p-value ≈   You have not attempted this yet 1.5 (.5 marks) Is the p-value less than the critical value? You have not attempted this yet 1.6 (.5 marks) Should we reject H0?

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 49% of all such batches contain no defective components, 27% contain one defective component, and 24% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.

no defective components:
one defective component:
two defective components	:

(b) One of the two tested components is defective. [Hint: Draw a tree diagram with three first-generation branches for the three different types of batches.]

no defective components
one defective component
two defective components

Consider two models that you are to fit to a single data set involving three variables: A, B, and C.

Model 1 : A ~B

Model 2 : A ~B + C

(a) When should you say that Simpson’s Paradox is occuring?

A. When Model 2 has a lower R2 than Model 1.

B. When Model 1 has a lower R2 than Model 2.

C. When the coef. on B in Model 2 has the opposite sign to the coef. on B in Model 1.

D. When the coef. on C in Model 2 has the opposite sign to the coef. on B in Model 1.

(b) True or False: If B is uncorrelated with A, then the coefficient on B in the model A ~ B must be zero.

(c) True or False: If B is uncorrelated with A, then the coefficient on B in a model A ~ B+C must be zero.

(d) True or False: Simpson’s Paradox can occur if B is uncorrelated with C.

3.4- Let Y1 = θ0 + ε1 and then for t > 1 define Yt recursively by Yt = θ0 + Yt−1 + εt. Here θ0 is a constant. The process {Yt} is called a random walk with drift.

(c) Find the autocovariance function for {Yt}.