Concept explainers
a.
Check whether the 95% confidence interval for the slope include zero. If so explain it and if not explain it.
a.
Answer to Problem 48CE
The 95% confidence intervaldoes not contain zero.
Explanation of Solution
Answer will vary.
Here the data set B is taken, in which the midterm exam and final exam score is given.
Regression:
Suppose
Where,
The total sum of squares is denoted as,
The regression sum of squares is denoted as,
The error sum of squares is denoted as,
From the regression the fitted line is denoted as,
The 95% confidence interval for the slope,
Where,
Procedure for 95% confidence interval using EXCEL:
Software Procedure:
Step-by-step software procedure to find 95% confidence interval using EXCEL software is as follows:
- • Open an EXCEL file.
- • In column A and B, the Midterm Exam Score and Final Exam Score data were entered.
- • Click on data > click on Data analysis.
- • Choose Regression > click OK.
- • Select Input Y range asthe column ofFinal Exam Score.
- • Select Input X range asthe column ofMidterm Exam Score.
- • Select the output range.
- • Click OK.
- Regression using EXCEL software is given below:
Thus, the 95% confidence interval of the slope is (0.7012, 1.3263).
Interpretation:
From the confidence interval it can be concluded that there is 95% confident that the slope will lie between 0.7012 and 1.3263.
The interval does not contain zero.
Theslope is not zero as the confidence interval does not contain zero.
b.
Perform a two-tailed t test for zero slope at
State the hypotheses, degrees of freedom and critical value for the test.
b.
Answer to Problem 48CE
There is nosufficient evidence to support that the slope is zero.
The hypotheses are:
Null hypothesis:
That is, the slope is zero.
Alternative hypothesis:
That is, the slope not equal to zero.
The degrees of freedom is56.
The critical value is
Explanation of Solution
Calculation:
Hypotheses:
Null hypothesis:
That is, the slope is zero.
Alternative hypothesis:
That is, the slope is not equal to zero.
From part(a), the test statistics is 6.498.
Critical value:
Here, the
The degrees of freedom is,
Thus, the degrees of freedom is56.
For two tailed test, the critical value for t-test will be,
It is assumed that the level of significance,
Procedure for critical-value using EXCEL:
Software Procedure:
Step-by-step software procedure to obtain critical-value using EXCEL software is as follows:
- • Open an EXCEL file.
- • In cell A1, enter the formula “=T.INV(0.025,56)”
- Output using EXCEL software is given below:
Here, the test is a two tailed test. Hence, the critical value will be
The level of significance is 0.05.
Decision rule:
If
If
Conclusion:
Here the test statistic value is greater than the critical value.
That is,
Hence, by the decision rule, reject the null hypothesis.
That is, the slope differs from zero.
Therefore, it can be concluded that there is nosufficient evidence to support that the slope is zero.
c.
Interpret the p-value for the slope.
c.
Explanation of Solution
From the output in part (a) it is observed that, the p-value for the slope is 0.000. That is, if midterm and final scores are not
d.
Check whether the sample support the hypothesis about the sign of the slope.
d.
Explanation of Solution
From part (b), there is no sufficient evidence to support that the slope is zero. Thus, the slope is either positive or negative. Hence, the sample supports the hypothesis about the sign of the slope.
Want to see more full solutions like this?
Chapter 12 Solutions
Loose-leaf For Applied Statistics In Business And Economics
- There are four white, fourteen blue and five green marbles in a bag. A marble is selected from the bag without looking. Find the odds of the following: The odds against selecting a green marble. The odds in favour of not selecting a green marble The odds in favor of the marble selected being either a white or a blue marble. What is true about the above odds? Explainarrow_forwardPlease show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy. 1. The probability of a soccer game in a particular league going into overtime is 0.125. Find the following: a. The odds in favour of a game going into overtime. b. The odds in favour of a game not going into overtime. c. If the teams in the league play 100 games in a season, about how many games would you expect to go into overtime?arrow_forwardexplain the importance of the Hypothesis test in a business setting, and give an example of a situation where it is helpful in business decision making.arrow_forward
- A college wants to estimate what students typically spend on textbooks. A report fromthe college bookstore observes that textbooks range in price from $22 to $186. Toobtain a 95% confidence level for a confidence interval estimate to plus or minus $10,how many students should the college survey? (We may estimate the populationstandard deviation as (range) ÷ 4.)arrow_forwardIn a study of how students give directions, forty volunteers were given the task ofexplaining to another person how to reach a destination. Researchers measured thefollowing five aspects of the subjects’ direction-giving behavior:• whether a map was available or if directions were given from memory without a map,• the gender of the direction-giver,• the distances given as part of the directions,• the number of times directions such as “north” or “left” were used,• the frequency of errors in directions. Identify each of the variables in this study, and whether each is quantitative orqualitative. For each quantitative variable, state whether it is discrete or continuous. Was this an observational study or an experimental study? Explain your answer.arrow_forwardexplain the difference between the confident interval and the confident level. provide an example to show how to correctly interpret a confidence interval.arrow_forward
- Sketch to scale the orbit of Earth about the sun. Graph Icarus’ orbit on the same set of axesWhile the sun is the center of Earth’s orbit, it is a focus of Icarus’ orbit. There aretwo points of intersection on the graph. Based on the graph, what is the approximate distance between the two points of intersection (in AU)?arrow_forwardThe diameters of ball bearings are distributed normally. The mean diameter is 67 millimeters and the standard deviation is 3 millimeters. Find the probability that the diameter of a selected bearing is greater than 63 millimeters. Round to four decimal places.arrow_forwardSuppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 22 Pennies 27 Dimes 9 Nickels 30 Quarters What is the probability that you reach into the jar and randomly grab a penny and then, without replacement, a dime? Express as a fraction or a decimal number rounded to four decimal places.arrow_forward
- A box contains 14 large marbles and 10 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 4 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or white? Express as a fraction or a decimal number rounded to four decimal places.arrow_forwardCan I get help with this step please? At a shooting range, instructors can determine if a shooter is consistently missing the target because of the gun sight or because of the shooter's ability. If a gun's sight is off, the variance of the distances between the shots and the center of the shot pattern will be small (even if the shots are not in the center of the target). A student claims that it is the sight that is off, not his aim, and wants the instructor to confirm his claim. If a skilled shooter fires a gun at a target multiple times, the distances between the shots and the center of the shot pattern, measured in centimeters (cm), will have a variance of less than 0.33. After the student shoots 28 shots at the target, the instructor calculates that the distances between his shots and the center of the shot pattern, measured in cm, have a variance of 0.25. Does this evidence support the student's claim that the gun's sight is off? Use a 0.025 level of significance. Assume that the…arrow_forwardThe National Academy of Science reported that 38% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 38%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 279 recent articles published by reputable mathematics research journals and finds that 123 of these articles have US authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 38 % ? Use a 0.02 level of significance. Compute the value of the test statistic. Round to two decimal places.arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman