Essentials of Statistics for the Behavioral Sciences
8th Edition
ISBN: 9781133956570
Author: Frederick J Gravetter, Larry B. Wallnau
Publisher: Cengage Learning
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Textbook Question
Chapter 4.5, Problem 1LC
Explain the difference between a biased and an unbiased statistic.
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Calculate the 90% confidence interval for the population mean difference using the data in the attached image. I need to see where I went wrong.
Microsoft Excel snapshot for random sampling: Also note the formula used for the last
column
02
x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
A
B
1
No.
States
2
1
ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
B
E
F
G
1
No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
sample
10
3
2 ALASKA
0.4493186 OKLAHOMA
k
5
4
3 ARIZONA
0.707914 KANSAS
5
4 ARKANSAS 0.4831379 NORTH DAKOTA
6
5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
9
8 DELAWARE 0.5783029 MISSOURI
525
10
15
INDIANA
MARYLAND
COLORADO
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined.
1.What percent of the refunds are more than $3,500?
2. What percent of the refunds are more than $3500 but less than $3579?
3. What percent of the refunds are more than $3325 but less than $3579?
Chapter 4 Solutions
Essentials of Statistics for the Behavioral Sciences
Ch. 4.3 - Brief explain what is measured by the standard...Ch. 4.3 - The deviation scores are calculated for each...Ch. 4.3 - What is the standard deviation for the following...Ch. 4.3 - Calculate the variance for the following...Ch. 4.3 - Find the sum of the squared deviations, SS, for...Ch. 4.3 - a. Sketch a histogram showing the frequency...Ch. 4.4 - a. Sketch a histogram showing the frequency...Ch. 4.4 - For the following set of scores: 1, 5, 7, 3, 4 a....Ch. 4.4 - Prob. 3LCCh. 4.5 - Explain the difference between a biased and an...
Ch. 4.5 - In a population with a mean of = 50 and a...Ch. 4.5 - A population has a mean of . = 70 and a standard...Ch. 4 - In words, explain what is measured by each of the...Ch. 4 - Can SS ever have a value less than zero? Explain...Ch. 4 - Is it possible to obtain a negative value for the...Ch. 4 - What does it mean for a sample to have a standard...Ch. 4 - Explain why the formula for sample variance is...Ch. 4 - A population has a mean of = 80 and a standard...Ch. 4 - On an exam with a mean of M = 78, you obtain a...Ch. 4 - Calculate the mean and SS (sum of squared...Ch. 4 - For the following population of N = 6 scores: 3 1...Ch. 4 - For the following sample of n = 7 scores: 8 6 5 2...Ch. 4 - For the following population of N = 6 scores: 11 0...Ch. 4 - The range is completely determined by the two...Ch. 4 - A population has a mean of = 30 and a standard...Ch. 4 - a. After 3 points have heen aikicd to every score...Ch. 4 - For the following sample of n = 4 scores: 82, 88,...Ch. 4 - For the following sample of n = 8 scores: 0, 1,...Ch. 4 - For the data in the following sample: 81515 a....Ch. 4 - Calculate the mean and SS (sum of squared...Ch. 4 - Calculate SS, variance, and standard deviation for...Ch. 4 - Calculate SS, variance, and standard deviation for...Ch. 4 - Calculate SS, variance, and standard deviation for...Ch. 4 - In an extensive study involving thousands of...Ch. 4 - Within a population, the difference that exist...Ch. 4 - In the previous problem we noted that the...Ch. 4 - a. What is the general goal for descriptive...
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- A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…arrow_forwardClient 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127arrow_forward
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