The foot size of each of 16 men was measured, resulting in the sample mean of 27.32 cm. Assume that the distribution of foot sizes is normal with sigma = 1.2 cm.

a) Test if the population mean of men’s foot sizes is 28.0 cm using alpha = 0.01.

b) If alpha = 0.01 is used, what is the probability of a type II error when the population mean is 27.0 cm?

c) Find the sample size required to ensure that the type II error probability beta(27) = 0.1 when alpha = 0.01.

Consider the value of t such that the area under the curve between −|t| and |t| equals 0.99.

Step 2 of 2:

Assuming the degrees of freedom equals 8, determine the t value. Round your answer to three decimal places.

Confidence Intervals

Do the calculations on paper. Show all work by writing the equation in symbol format first. Then define each symbol in terms of the problem. Show each step of your calculation, skipping no step (each division, each addition, each multiplication.) When you have your final answer(s), draw a box around them. Copy and paste the image(s) into your document and label the image(s.) [That is to say, some people write larger, some smaller, some may get the work to fit nicely on half a page, others may take two and a half pages... Grade not based on how many pages... Grade based on reasonable work which can be read and followed. If you type it out, great. But if you do not, also great. Still show all work, no skipped steps.] Use software to replicate your answers. Paste in output to verify software use. [Excel, Minitab, StatCrunch, other apps...as your choice, just reference what you used...if on a page, give hyperlink to page, but do make sure you paste in work.]

Then explain your answer in words. Make a confidence statement. Explain its limitations, and its risks. [how sure are you that you are right; what are the costs and probability that you are wrong.

A1 Eddie is the manager of a small grocery store in Alabama, which is part of a large chain, but serves a rural community. His store had begun offering online ordering, with store parking lot pickup last year. It was not a big thing, as so many people socialized when they "came to town to shop. This last month, things have changed. More of his regular customers are doing online shopping/parking lot pickup. He did a random sample from the last two weeks, choosing a sample of 49 from the 589 orders. The mean of his sample was $85.00, with a standard deviation of $15.00.  Choose a confidence interval [80, 90, 95, or 99] and explain why that percent would work for this question.   Create a confidence interval of the mean to predict the average dollar of sales. Make a statement, using the results from your calculations, rounding reasonably.

1. A political scientist is interested in the question of whether or not there is a difference between Republicans and Democrats when it comes to their involvement in voluntary associations. Using a 25-point scale to measure involvement in voluntary associations, and collecting information from a random sample of 17 Republicans and 12 Democrats, the political scientist discovers the following:

Republicans: Mean of 12.56, standard deviation of 3.77

Democrats: Mean of 16.43, standard deviation of 4.21

Test the null hypothesis at the .05 level of significance.

1. State the null and alternative hypotheses (1 pt).

2. Write what a Type I error would be in the context of this problem (1 pt).

3. Write what a Type II error would be in the context of this problem (1 pt).

4. Write what Power is in context of this problem (1 pt).

e. Compute the effect size (Cohen’s d) (1 pt).

A company wants to determine whether its consumer product ratings

​(0minus−​10)

have changed from last year to this year. The table below shows the​ company's product ratings from eight consumers for last year and this year. At

alphaαequals=​0.05,

is there enough evidence to conclude that the ratings have​ changed? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (f).

Question 1. The numbers 5, 8, 10, 7, 10, and 14 gather from a simple random sample of a population. Determine/Calculate the point estimate of the population mean (or worded another way, what is the sample mean, x-bar,?). Determine/Calculate the point estimate of the population standard deviation (or worded another way, what is the sample standard deviation, s,?).

Question 2. A population has a mean of 200 dollars earned a day and a standard deviation of 50 dollars a day. Suppose a simple random sample was taken of 100 people (note: n > 30 so we can assume standard distribution) and we used x-bar (sample mean) to estimate mu (population mean). What is the probability that the sample mean will be within +/- 5 of the population mean? What is the probability that the sample mean will be within +/- 10 of the population mean?

Question 3. A population proportion was determined to be 0.40. A simple random sample was taken of 200 people will be taken and the sample proportion, p-bar, will be used to estimate the population proportion (which we already know is 0.40). What is the probability that the sample proportion (p-bar) will be within +/- 0.03 of the population proportion? What is the probability that the sample proportion (p-bar) will be within +/- 0.05 of the population proportion?

For which of the following research questions could you test using a dependent samples t-test? Group of answer choices Do student athletes and non student athletes differ on levels of self-esteem? Is there a difference in verbal problem solving skills between science majors and art majors? Is pain tolerance different with acupuncture versus without acupuncture needles? Do boys and girls differ on mathematical abilities?

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped with a mean of 37 ounces and a standard deviation of 3 ounces. Using the Empirical Rule, answer the following questions. Suggestion: Sketch the distribution.

a) 95% of the widget weights lie between  and

b) What percentage of the widget weights lie between 28 and 43 ounces?  %

c) What percentage of the widget weights lie below 40?  %

Potatoes: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 9 ounces and a standard deviation of 1.1 ounces. (a) Carl only wants to sell the best potatoes to his friends and neighbors at the farmer's market. According to weight, this means he wants to sell only those potatoes that are among the heaviest 5%. What is the minimum weight required to be brought to the farmer's market? Round your answer to 2 decimal places. ounces (b) He wants to use the lightest potatoes as ammunition for his potato launcher but can only spare about 5% of his crop for such frivolities. What is the weight limit for potatoes to be considered for ammunition? Round your answer to 2 decimal places. ounces (c) Determine the weights that delineate the middle 95% of Carl's potatoes from the others. Round your answers to 2 decimal places.

1. For each of the data described below (a – e) specify whether the data is:

 Quantitative or Categorical

 Continuous, Discrete, or this distinction is not applicable

 Variable or Attribute

 Ratio, Interval, Ordinal, or Nominal

a. Data collected about whether the advice given to a customer who called into a call center resulted in resolution of the customer’s software problem or not

b. The number of customers served each day at the Boehly Café

c. The number gallons of heating oil delivered to residences

d. The country of origin for people who work for a particular company

e. A JD Power listing of the top 10 midsize automobiles in order of consumer feedback

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 equals n=951 and x equals x=543 who said​ "yes." Use a 90% confidence level.

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

E=

c) Construct the confidence interval

You are asked to study the determinants of job satisfaction at your new company. After randomly selecting 40 employees to fill out a questionnaire you regress their job satisfactions score (JOBSAT) on the following variables: SCHOOL = years of schooling MALE = 1 if male Engr = 1 if employee is in the technical division Adv = 1 if employee is in the marketing division Sales = 1 if employee is in the sales division Exec = 1 if employee is in the corporate division Some regression output is attached following the questions below: a) Test whether any of the explanatory variables are related to job satisfaction b) Test the hypothesis that schooling affects job satisfaction c) Give a confidence interval for the coefficient for the MALE variable. What does the interval imply about male versus female job satisfaction? d) Test whether an employee’s job satisfaction depends on the department where they work 4 e) When explaining your results to your boss, she questions whether you performed your analysis correctly since there are four departments in your firm but you only included variables for three departments. How would you respond?

The regression equation is JOBSAT = 51.8 + 3.48 MALE + 0.504 SCHOOL + 6.06 Engr -0.37 Adv +2.99 Sales

Predictor Coef Stdev t-ratio

Constant 51.798 6.888 7.52

MALE 3.484 1.558 2.24

SCHOOL 0.504 0.478 1.05

Engr 6.055 2.219 2.73

Adv -0.370 2.308 -0.16

Sales 2.987 2.190 1.36

s = 4.869 R-sq = 35.3% R-sq(adj) = 25.8%

Analysis of Variance

SOURCE DF SS MS F p

Regression 5 440.18 88.04 3.71 0.009

Error 34 805.89 23.70

Total 39 1246.07

The regression equation is JOBSAT = 53.8 + 3.48 MALE + 0.517 SCHOOL

Predictor Coef Stdev t-ratio

Constant 51.794 6.677 8.06

MALE 3.477 1.723 2.02

SCHOOL 0.517 0.498 1.04 s = 5.390 R-sq = 13.7% R-sq(adj) = 9.1%

Analysis of Variance

SOURCE DF SS MS F p

Regression 2 171.18 85.50 2.94 0.065

Error 37 1075.08 29.06

Total 39 1246.07

The Club has 9 members. The club needs to elect a President, Vice President, Secretary and Treasurer, how many different ways are possible? How many ways are there to find a committee of size three.

The Club has 10 members, 3 freshman, 4 sophomores and 3 juniors. How many ways are there to find a committee of size three with no freshmen? How many ways are there to find a committee of size three with one freshmen?

Gasoline mileage (mpg) was measured on several cars of each of four different makes (coded 1, 2, 3 and 4). The make of each car is stored in the first column, and the mileage for each car is stored in the second column, of Table A. You need to conduct an analysis of variance to see if there are differences among the four makes in gasoline mileage. You should also estimate the mileage of each of the four makes of cars.
1. What is the value of the F‑statistic for testing the null hypothesis that there are no differences in gasoline mileage among the four makes of automobile?
2. What are the degrees of freedom associated with the numerator of this test statistic?
3. What are the degrees of freedom associated with the denominator of the F‑value for MAKE of car?
4. What is the estimate of the pooled variance within makes of cars (i.e. the Error mean square)?
5. What are the degrees of freedom for this variance in #4?