A psychologist is examining the educational advantages of a preschool program and suspects that there will be significant (α = .01) differences in achievement among 4th graders based on whether or not they attended preschool. Twenty-three randomly selected 4th grade children are used in the study. Twelve attended a preschool program and eleven did not (see the data below).

Group 1 - Preschool: 8, 6, 8, 9, 7, 9, 6, 9, 8, 9, 7, 8

Group 2 - No Preschool: 6, 5, 7, 6, 8, 5, 7, 5, 6, 7, 5

What is the alternative hypothesis for this independent samples t-test?

Group of answer choices µ1 - µ2 ≥ 0 µ1 - µ2 = 0 µ1 - µ2 ≠ 0 µ1 - µ2 ≤ 0 µ1 - µ2 µ1 - µ2 > 0

Golf and Chi-Square Tests

Discussion

Introduction

This discussion provides a simulated exercise using two of the most popular Chi-Square statistical tests. You are strongly encouraged to complete the textbook reading and start the MyStatLab Homework assignment before beginning this discussion. You need to be familiar with the Chi-Square distribution, its interpretation, and how results are typically calculated and reported together.

In this discussion, you are required to calculate and interpret your findings.

Review the information in each section and participate in the discussion.

Golf Rounds Scenario

As the Director of Golf for the Links Group, you are trying to determine if there is a significant difference in the number of rounds of golf played based on the day of the week. So far, you've gathered the following sample information for 520 rounds.

Now, you need to use the sample to answer these questions. For each question, the null hypothesis is that the cell categories are equal, and the significance level is .05.

• Is there a significant difference in the rounds of golf played during the week? Why is your choice appropriate?
• What is the critical value and number of degrees of freedom for the Chi-Square statistic?
• What is your decision regarding the null hypothesis? Why is your decision appropriate?

Golf Ball Quality Scenario

In addition to determining if there is a significant difference in the number of rounds of golf played based on the day of the week, you also have to determine which brand of "range balls" to buy for use at the driving range. You are looking for the most durable ball that will hold up for an extended period. You obtained samples of 100 golf balls from four different manufacturers, and your teaching professionals tested them for durability. The table shows the numbers of unacceptable and acceptable golf balls by manufacturer.

At the .05 significance level, is there a difference in the durability of the range balls? Why is your decision appropriate?

Additional Instructions

Use Excel or Statdisk to answer the questions posed in both scenarios. Remember, the focus of this discussion is understanding and interpreting two different Chi-Square tests.

6. A calculated correlation coefficient of 0.99 between variables A and B implies that variable A causes variable B.

7. Which of the following is NOT a possible value for a calculated F statistic?

8. A large student organization at CSUN claims it has an equal distribution of people from each of the 9 colleges (e.g., business, humanities). You are interested in investigating whether or not this claim is accurate. To do so, you first take a sample of students from the organization. What would be the most appropriate test to utilize with your sample data to help answer this research question?

9. You are presented with 4 different correlation coefficients (r): 0.65, -0.34, -0.86, and 0.19. Which of the following lists correctly represents the 4 r’s placed in order of strength from weakest to strongest.

10.

In which direction is the χ² (chi-square) distribution skewed?

The National Collegiate Athletic Association (NCAA) requires Division II athletes to score at least 820 on the combined mathematics and reading parts of the SAT in order to compete in their first college year. The scores of the 1.5 million high school seniors taking the SAT last year are approximately Normal with mean 1026 and standard deviation 209. For an SRS size 200

1) Find the mean and standard deviation of x bar

2) What is the distribution of x bar?

3) What is the probability that a sample mean value exceeds 1028?

4) The highest 2.5% of sample mean value are higher than ____

5) Has the average score increased since last year? To answer this, do the followings:

I. A SRS size 200 gives a sample mean of 1028. State hypotheses, find the test statistic, pvalue, and express your conclusion using a significance level of α=2.5%.

a. Hypotheses (Use notations)

b. test statistic

c. pvalue

d. Conclusion? Include practical terms.

II. Find a 95% confidence interval for the mean SAT score.

A company uses a combination of three components- A, B and C to create three different drone designs. The first design Glider uses 3 parts of component A and 2 parts of components B. Design Blimp uses 2 parts of component B and C, and the last design, Pilot uses one part of each component. A sample of 75 components, 25 A, 25 B, 25 C, will be used to make prototypes for the various designs. If 30 components are selected at random, what is the likelihood two prototypes of each design can be made?

You may need to use the appropriate technology to answer this question.

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = 0.05.

Find the value of the test statistic for method of loading and unloading.

Find the p-value for method of loading and unloading. (Round your answer to three decimal places.)

p-value =

State your conclusion about method of loading and unloading.

Because the p-value > α = 0.05, method of loading and unloading is not significant.Because the p-value ≤ α = 0.05, method of loading and unloading is significant.     Because the p-value ≤ α = 0.05, method of loading and unloading is not significant.Because the p-value > α = 0.05, method of loading and unloading is significant.

Find the value of the test statistic for type of ride.

Find the p-value for type of ride. (Round your answer to three decimal places.)

p-value =

State your conclusion about type of ride.

Because the p-value ≤ α = 0.05, type of ride is not significant.Because the p-value ≤ α = 0.05, type of ride is significant.     Because the p-value > α = 0.05, type of ride is not significant.Because the p-value > α = 0.05, type of ride is significant.

Find the value of the test statistic for interaction between method of loading and unloading and type of ride.

Find the p-value for interaction between method of loading and unloading and type of ride. (Round your answer to three decimal places.)

p-value =

State your conclusion about interaction between method of loading and unloading and type of ride.

Because the p-value > α = 0.05, interaction between method of loading and unloading and type of ride is significant.Because the p-value > α = 0.05, interaction between method of loading and unloading and type of ride is not significant.     Because the p-value ≤ α = 0.05, interaction between method of loading and unloading and type of ride is significant.Because the p-value ≤ α = 0.05, interaction between method of loading and unloading and type of ride is not significant.

2. You may need to use the appropriate technology to answer this question.

The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST = 282, SSA = 26, SSB = 22, SSAB = 179.Set up the ANOVA table. (Round your values for mean squares and F to two decimal places, and your p-values to three decimal places.)

Test for any significant main effects and any interaction effect. Use α = 0.05.

Find the value of the test statistic for factor A. (Round your answer to two decimal places.)

Find the p-value for factor A. (Round your answer to three decimal places.)

p-value =

State your conclusion about factor A.

Because the p-value ≤ α = 0.05, factor A is not significant.Because the p-value ≤ α = 0.05, factor A is significant.     Because the p-value > α = 0.05, factor A is not significant.Because the p-value > α = 0.05, factor A is significant.

Find the value of the test statistic for factor B. (Round your answer to two decimal places.)

Find the p-value for factor B. (Round your answer to three decimal places.)

p-value =

State your conclusion about factor B.

Because the p-value ≤ α = 0.05, factor B is significant.Because the p-value ≤ α = 0.05, factor B is not significant.     Because the p-value > α = 0.05, factor B is not significant.Because the p-value > α = 0.05, factor B is significant.

Find the value of the test statistic for the interaction between factors A and B. (Round your answer to two decimal places.)

Find the p-value for the interaction between factors A and B. (Round your answer to three decimal places.)

p-value =

State your conclusion about the interaction between factors A and B.

Because the p-value > α = 0.05, the interaction between factors A and B is not significant.Because the p-value ≤ α = 0.05, the interaction between factors A and B is not significant.     Because the p-value ≤ α = 0.05, the interaction between factors A and B is significant.Because the p-value > α = 0.05, the interaction between factors A and B is significant.

Find the critical value of t for each of the following:

Please show work and explain.

a. 1-α = 0.95, n=21

b. 1-α = 0.99, n=21

c. 1-α = 0.90, n=32

d. 1-α = 0.99, n=65

The researcher from problem 1 has a graduate student who is exploring doing his master's degree in the area of community-based mental health services. The student wants to assess whether the public health agencies in the southern part of the state have fewer resources than the agencies in the northern part of the state. He obtained survey data from a convenience sample of 12 agencies, 6 from the northern region and 6 from the southern region. The survey items used this response scale about their funding: 3 = more than enough funding, 2 = about enough funding, 1 = not enough funding (the survey did not interval level data). Here are the data:

Northern: 3, 3, 2, 1, 3, 2

Southern: 2, 1, 3, 2, 1, 2

A machine produces coins such that the probability of heads, p, follows a Beta distribution with parameters (α, β) = (1, 1). A coin produced by this machine is picked at random and tossed independently n times. Let Y be the number of heads.

1. (a) Find E[Y ].

2. (b) Write down the pmf for Y (your answer can include unevaluated integrals and

   combination numbers [aka “n choose m” symbols]).

Question 3:

Suppose that 1000 customers are surveyed and 850 are satisfied or very satisfied with a corporation’s products and services.

1. Test the hypothesis H₀: p = 0.9 against H₁: p ≠ 0.9 at α = 0.05. Find the p-value.
2. Explain how the question in part (a) could be answered by constructing a 95% two-sided confidence interval for p.

W71) I am study Excel Functions. Please answer in detail using Excel functions.

Parking Tickets – The Chicago police department claims that it issues an average of only 60 parking tickets per day. The data below, reproduced in your Excel answer workbook, show the number of parking tickets issued each day for a randomly selected period of 30 days. Assume σ =13.42.   State the null and alternate hypotheses, as well as the claim, which (hint!) is in the null hypothesis. Is there enough evidence to reject the group’s claim at α = .05?   (As with all of these exercises, use the P-value method, rounding to 4 digits.) (Hint: so since we know the population standard deviation, use the standard normal distribution z-test .) (Monday class)

              79         78         71         72         69         71              57         60

              83         36         60         74         58         86              48         59

              70         66         64         68         52         67              67

              68         73         59         83         85         34              73

We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different “digits” {0,1,…,9}.{0,1,…,9}. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0,1,…,9,A,B,C,D,E,F}.{0,1,…,9,A,B,C,D,E,F}. So for example, a 3 digit hexadecimal number might be 2B8.

How many 3-digit hexadecimals are there in which the first digit is E or F?

How many 4-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?

How many 4-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)?

In a recent survey, 43 students reported whether they liked their potatoes Mashed, French-fried, or Twice-baked. 24 liked them mashed, 23 liked French fries, and 12 liked twice baked potatoes. Additionally, 11 students liked both mashed and fried potatoes, 9 liked French fries and twice baked potatoes, 10 liked mashed and baked, and 2 liked all three styles. How many students hate potatoes? Explain why your answer is correct.

How many positive integers less than 975 are multiples of 8, 7, or 9? Use the Principle of Inclusion/Exclusion.

We want to build 5 letter “words” using only the first n=12n=12 letters of the alphabet. For example, if n=5n=5 we can use the first 5 letters, {a,b,c,d,e}{a,b,c,d,e} (Recall, words are just strings of letters, not necessarily actual English words.)

1. How many of these words are there total?
2. How many of these words contain no repeated letters?
3. How many of these words start with the sub-word “ade”?
4. How many of these words either start with “ade” or end with “be” or both?
5. How many of the words containing no repeats also do not contain the sub-word “bed”?

1. If all the letters of the word ABOUT are arranged at random in a line, find the probability that the arrangement will begin with AB...

2.   

The odds of throwing two fours on a single toss of a pair of dice is 1:35
What is the probability of not throwing two fours? (Hint: there are 2 conversions here)

All answers are written as fractions for consistency....

Select one:

a. 35/36

b. 1/36

c. 1/35

d. 35/1

Discuss the real–world applications where probabilities are used. (Ex. Stock market trading; Medical treatment plans; etc.)

The null hypothesis plays an important role in significance testing. Explain the concept underlying the null hypothesis and the role it plays in tests of statistical significance (hint: think of the logic involved in the decision making process).