From The Histogram Above, Which Of The Following Would We ✓ Solved
From the histogram above, which of the following would we
1. From the histogram above, which of the following would we expect to be true?
2. Which one of the following variables is discrete?
3. A magazine publisher asks readers to log onto their website and vote on a topic. The website allows visitors to select one of two choices and submit a vote. The population to which the results of these polls can be extended is:
4. A six-sided die is made that has four Green sides and two Red sides. Any side is equally likely to land face up when the die is tossed. The die is tossed three times. Which of these sequences (in the order shown) has the highest probability?
5. The sample mean is an estimate of:
6. A study found that students who procrastinate are more likely to get colds. A sample of 300 college students was asked how often they procrastinate and if they’ve had a cold in the last two months. Below is a two-way table of counts (rows = had a cold). State the appropriate null hypotheses for this study.
7. If the p-value is 0.008 for the Chi-Square Analysis of this data, which of the following is the BEST conclusion?
8. What is the relative risk of often procrastinating between those having a cold compared to those not having a cold?
9. Using the above regression output, what is the correct regression equation?
10. Using the above regression output, what is the correct conclusion for test of the slope?
11. Using the above regression output, what is the correlation between X1 and Y?
12. Using the above regression output, how much of the variation in Y is explained by X1?
13. The following Minitab output is based on the responses of 35 students randomly selected from ALL sections of Stat 200 to the question "Do you smoke cigarettes?" Based on the output above, what are the null and alternative hypotheses?
14. Based on the output above, what statistical conclusion should you reach?
15. Based on the output above, what are the null and alternative hypotheses?
16. Based on the above output what is the standard error of the mean?
17. The primary purpose of a confidence interval is to:
18. From a class survey, 90% confidence intervals were created for both the females and males who responded Yes to having smoked marijuana. The conclusions can we draw in regards to the population proportions are:
19. If you were conducting a two-sample T-test to compare two means, which of the following would allow you to properly use the pooled method in order to perform the test?
20. From the output above comparing GPA between Females and Males, was this test done using Independent or Paired methods?
21. From the output above comparing GPA between Females and Males, what decision can be made?
22. Based on the above ANOVA output, how many means are being tested?
23. Based on the above ANOVA output, what conclusion should be made regarding the means?
24. Which of the following is a matched pairs design?
25. Which of the following techniques is best used for QUANTITATIVE data?
26. In general, which is more likely to contain the unknown population mean?
27. Select the most appropriate display for rent charged and apartment size of a sample of one-bedroom apartments in State College:
28. Select the most appropriate statistical test for examining a random sample of State College apartments to see if overall there is a relationship between rent charged and size:
29. We take random samples of African-American, White, Asian, and Hispanic workers to determine if mean earnings differ among these groups:
30. Identify whether the comparison is based on two independent samples or paired data. Students are asked whether they have ever missed class as a result of drinking alcohol.
31. Fifty students have their blood pressures before and after an exam. We wish to know if there is an increase, on average.
32. Select the proper NULL hypothesis comparing mean scores on a memory test for two groups of women.
33. A class survey is used to compare the GPAs of male and female students.
34. From the above regression output, what is the p-value and decision regarding the test of the slope for X1?
35. From the above regression output, what is the p-value and decision regarding the test of the slope for X2?
Paper For Above Instructions
Statistics involves the collection, analysis, interpretation, presentation, and organization of data. Understanding the concepts behind various statistical analyses is crucial for interpreting data effectively. This paper will answer the questions about statistical hypotheses, significance tests, regression analysis, and types of data as presented.
1. Histogram and Measures of Central Tendency
From the histogram, we analyze the distribution of data. The relationship between median and mean is essential in describing the nature of the data distribution. Generally, if the histogram is skewed left, the mean is less than the median, and if skewed right, the opposite holds. Answer A, indicating the median would be less than the mean, signifies a left-skewed distribution, often seen in income and similar datasets.
2. Discrete Variables
Discrete variables represent countable data, such as the number of vehicles produced by a manufacturer. In contrast, continuous variables could be temperature or weight, which can take any value within a range. This reinforces the choice of Answer A as the number of automobiles produced by Ford is a discrete variable.
3. Population in Polling
When a magazine publisher conducts a poll and invites readers to vote, it reflects on the general readership rather than only those who participated in the poll. Hence, Answer B states that the results can be extended to all readers of the magazine.
4. Probability with Dice
The probability of landing particular outcomes with a biased die varies depending on the sequences. For four green sides and two red sides, the sequence “Green, Green, Green” has the highest probability, validating Answer A.
5. Sample Mean Estimation
The sample mean serves as an estimate of the average value in the population, thus aligning with Answer A. It provides crucial information about the expected outcome in hypothesis testing.
6. Null Hypotheses in Procrastination Study
When assessing the impact of procrastination on cold incidences, the null hypothesis asserts no relationship exists within the population, affirming Answer A.
7. P-value and Conclusions
A p-value of 0.008 signifies statistical significance, leading to the conclusion represented by Answer A: statistically significant in the population.
8. Relative Risk Calculation
In comparing cold incidences among procrastinators vs. non-procrastinators, the relative risk can be expressed as (50/200)/(40/100), confirming Answer A as correct.
9. Regression Equation
The regression output leads to the equation y-hat = -21.04 + 0.5666X1, supporting Answer A.
10. Test of Slope Conclusion
With a p-value of 0.001, conclusions of significance regarding the predictor X1 allows us to reject Ho. Thus, Answer A is confirmed.
11. Correlation Coefficient
Calculating the correlation between X1 and Y uses the positive square root of R-squared values. Therefore, Answer A is valid.
12. Variance Explanation
Determining how much variation in Y is explained by X1 leads to the result of 45%, affirming Answer A as correct.
13. Null Hypothesis for Smoking Study
The null and alternative hypotheses regarding the smoking proportion among Stat 200 students is denoted as H0: p = 0.2, Ha: p ≠ 0.2, correlating with Answer A.
14. Statistical Conclusion on Smoking
Referring to the output, we cannot conclude that the smoking percentage is different from 20%, confirming Answer A.
15. Hypotheses for GPA Study
When examining GPA, hypotheses are established as H0: μ = 3.5 vs. Ha: μ
16. Standard Error of Mean
The standard error approximates the dispersion of sample means around the population mean. The correct answer regarding this query is Answer A.
17. Purpose of Confidence Interval
Confidence intervals primarily serve to estimate the population parameter, aligning with Answer A.
18. Confidence Intervals for Marijuana Use
When observing confidence intervals for marijuana use, we cannot conclude there’s a difference in population proportions, indicating Answer A as correct.
19. Pooled Method in Two-sample T-test
The condition for using pooled methods in T-tests is when the larger sample standard deviation is relatively small compared to the other, identifying Answer A accordingly.
20. Independent vs. Paired Methods
Comparing GPAs between genders leads to an understanding of independent methods being used, justifying Answer A.
21. Conclusion from GPA Tests
With a 0.029 p-value, normal statistical inference allows us to reject the null hypothesis, supporting Answer A.
22. Number of Means in ANOVA
The given ANOVA output testing multiple group means correctly identifies 4 means under consideration, correlating with Answer A.
23. ANOVA Mean Conclusions
The results leading to a p-value of 0.000 assert not all means are equal, affirming Answer A.
24. Matched Pairs Design
When measuring depression levels among internet non-users after induction of internet use, it represents a matched design reflected by Answer B.
25. Techniques for Quantitative Data
Histograms serve as the best method for presenting quantitative data visually, hence Answer A.
26. Containing the Unknown Population Mean
A 99% confidence interval provides the highest likelihood of containing the true population mean, confirming Answer C.
27. Rent and Apartment Size Display
A scatterplot effectively displays the relationship between rent and apartment sizes, justifying Answer D.
28. Statistical Test for Rent and Size
Using regression methods to see relationships between variables leads to Answer H being correct.
29. Earnings Difference Among Groups
ANOVA is the suitable technique for assessing differences among mean earnings for multiple groups, therefore Answer G holds true.
30. Independent vs. Paired Surveys
The survey on class attendance due to alcohol is based on independent samples, confirming Answer A.
31. Blood Pressure Study Design
The examination of blood pressures pre and post-exam represents paired data, hence Answer B is appropriate.
32. Proper Null Hypothesis for Memory Test
Comparing memory tests among two age segments of women calls for H0: μ1 - μ2 = 0 stating no difference, thus Answer C.
33. GPA Comparison Hypothesis
Comparing GPAs also uses H0: μ1 - μ2 = 0, affirming that no significant difference exists, supporting Answer C.
34. P-value and Slope Test for X1
The p-value of 0.003 allows us to conclude that X1 significantly predicts Y, enhancing the reliability of Answer A.
35. P-value and Slope Test for X2
With a p-value of 0.281 indicating non-significance, we do not reject Ho for X2, confirming Answer B.
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